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FINDING THE SURFACE AREA OF A COMPOSITE SOLID

About "Finding the surface area of a composite solid"

Finding the surface area of a composite solid :

A composite solid is made up of two or more solid figures.

To find the surface area of a composite solid, find the surface area of each figure. Subtract any area not on the surface.

Finding the surface area of a composite solid - Examples

Example 1 :  

Daniel built the birdhouse shown below. What was the surface area of the birdhouse before the hole was drilled ?

Solution :  

Step 1 :

Identify the important information.

• The top is a triangular prism with h = 24 cm. The base is a triangle with height 8 cm and base 30 cm.

• The bottom is a rectangular prism with h = 18 cm. The base is a 30 cm by 24 cm rectangle.

• One face of each prism is not on the surface of the figure.

Step 2 :  

Find the surface area of each prism.

Add the areas. Subtract the areas of the parts not on the surface.

Step 3 :  

Find the area of the triangular prism.

Perimeter  =  17 + 17 + 30  =  64 cm

Base area  =  (1/2)(30)(8)  =  120 sq.cm

Surface area  =  Ph + 2B

Surface area  =  64(24) + 2(120)

Surface area  =  1,776 sq.cm

Step 4 :  

Find the area of the rectangular prism.

Perimeter  =  2(30) + 2(24)  =  108 cm

Base area  =  30(24)  =  720 sq.cm

Surface area  =  Ph + 2B

Surface area  =  108(18) + 2(720)

Surface area  =  3,384 sq.cm

Step 5 :  

Add. Then subtract twice the areas of the parts not on the surface.

Surface area  =  1,776 + 3,384 - 2(720)  =  3,720 sq.cm

The surface area before the hole was drilled was 3,720 sq.cm.

The surface area before the hole was drilled was; 3,720 sq.cm.

A composite solid is made up of two or more solid figures.

To determine the surface area of a composite solid, find the surface area of each figure. Subtract any area not on the surface.

Given that the top is a triangular prism with h = 24 cm. The base is a triangle with height 8 cm and base 30 cm.

The bottom is a rectangular prism with h = 18 cm.

The base is a 30 cm x 24 cm rectangle.

One face of each prism is not on the surface of the figure.

Then the surface area of each prism.

Add the areas. Subtract the areas of the parts not on the surface.

The area of the triangular prism.

Perimeter  =  17 + 17 + 30  =  64 cm

Base area  =  (1/2)(30)(8)  =  120 sq.cm

Surface area  =  Ph + 2B

Surface area  =  64(24) + 2(120)

Surface area  =  1,776 sq.cm

Now the area of the rectangular prism.

Perimeter  =  2(30) + 2(24)  =  108 cm

Base area  =  30(24)  =  720 sq.cm

Surface area  =  Ph + 2B

Surface area  =  108(18) + 2(720)

Surface area  =  3,384 sq.cm

Now,

Surface area  =  1,776 + 3,384 - 2(720)  =  3,720 sq.cm

Learn more about the area;

https://brainly.com/question/1658516

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(a)

[tex] \sqrt[5]{ {x}^{3} } [/tex]

(b)

[tex] \sqrt[8]{x} [/tex]

(c)

[tex] \sqrt[3]{ {x}^{5} } [/tex]

(d)

[tex] \sqrt{ {x}^{3} } [/tex]

Answer:

(71.28, 78.72)

Step-by-step explanation:

We have the following information from the statement:

mean (m) = 75

sample standard deviation (sd) = 5

Sample size (n) = 13

Significance level (alpha) = 1 - 0.98 = 0.02

Degrees of freedom for t-d (df) = n - 1 = 13 - 1 = 12

The critical value would be:

t (alpha / 2) / df = T (0.01) / 12 = 2,681 (this for the table)

Margin of error equals:

E = t (alpha / 2) / df * sd / n ^ (1/2), replacing:

E = 2,681 * 5/13 ^ (1/2)

E = 3.72

Therefore, the interval of 98% confidence interval would be:

75 + 3.72 = 78.72

75 - 3.72 = 71.28

(71.28, 78.72)

Answer:

5.5 hours

Step-by-step explanation:

We have that the distance is given by:

d = v * t = 50 mph * 1/2 h = 25 miles

The relative speed is given by:

 vr = 55 mph - 50 mph = 5 mph

Now the time required to reach

 would come being:

t = t '+ d / vr

we know that t '= 1/2 h, replacing:

t = 1/2 h + 25 mi / 5 mph

t = 1/2 h + 5 h

t = 5.5 h

Therefore, the required time is 5.5 hours.

Answer:

14.28 mm

Step-by-step explanation:

Find the circumference if it were a normal circle, then divide it by 4.

C = 2[tex]\pi[/tex]r

C = 2[tex]\pi[/tex](4)

C = 8[tex]\pi[/tex]

Divide it by 4

2[tex]\pi[/tex] + 4 + 4 = 14.28

Answer:

25.13 mm is the circumfrence, I believe.. Been a while since I've worked with this

Step-by-step explanation:

Answer:

Percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg = 78.5%

The sampling error is 0.08083, in terms of the sampling error, 78.5% of samples of three men will have mean brain weights within (1.24×sampling error) of the mean.

Step-by-step explanation:

Complete Question

According to one study, brain weights of men are normally distributed with mean = 1.20 kg and a standard deviation = 0.14 kg.

Determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg. Interpret your answer in terms of sampling error.

Solution

The Central limit theorem allows us to say

The mean of sampling distribution is approximately equal to the population mean.

μₓ = μ = 1.20 kg

And the standard deviation of the sampling distribution is given as

σₓ = (σ/√N)

σ = population standard deviation = 0.14 kg

N = sample size = 3

σₓ = (0.14/√3) = 0.08083

Percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg, that is, percentage of all samples of three men with mean brain weights within 1.10 kg and 1.30 kg.

P(1.10 ≤ x ≤ 1.30)

We first normalize or standardize 1.10 and 1.30

The standardized score for any value is the value minus the mean then divided by the standard deviation.

For 1.10 kg

z = (x - μₓ)/σₓ = (1.10 - 1.20)/0.08083 = -1.24

For 1.30 kg

z = (x - μₓ)/σₓ = (1.30 - 1.20)/0.08083 = 1.24

To determine the required probability

P(1.10 ≤ x ≤ 1.30) = P(-1.24 ≤ z ≤ 1.24)

We'll use data from the normal distribution table for these probabilities

P(1.10 ≤ x ≤ 1.30) = P(-1.24 ≤ z ≤ 1.24)

= P(z ≤ 1.24) - P(z ≤ -1.24)

= 0.89251 - 0.10749

= 0.78502 = 78.502%

The sampling error is 0.08083, in terms of the sampling error, 78.5% of samples of three men will have mean brain weights within (1.24×sampling error) of the mean.

Hope this Helps!!!

Answer: itz 605

Step-by-step explanation:

Answer:

a) Experimental Design:  Randomised Experimental Design

b) Population : All Adult outpatients diagnosed with major depression

c) Responsive Variable : Effectiveness of extracts on depression patients' HAM-D rating

d) Treatments : John Wart extracts or Placebo

e) Experimental units : 200 adult outpatients diagnosed with major depression having HAM-D score > 20

Step-by-step explanation:

a) Randomised Experimental Design is being used : As experimental units are randomly assigned to any of the experimental groups, each receiving different treatments

b) Population refers to the entire group of objects or individuals, to whom the experiment research can be applied. So, all adult outpatients diagnosed with major depression as per HAM-D depression score are population

c) Responsive variable is the dependent variable being affected by independent variables. It is effectiveness of extracts on depression patients, ie change in change on the HAM-D depression rating

d) Treatments are the ways or objects with which experimental units are treated. These are John wart extracts or Placebo

e) Experimental units are the selected sample people or objects for experiment conduct. These are '200' adult outpatients diagnosed with major depression, having a baseline Hamilton Rating Scale for Depression (HAM-D) score > 20

Answer:

x = -3

Step-by-step explanation:

1.8 - 3.7x = -4.2x +.3

Add 4.2x to each side

1.8 - 3.7x +4.2x= -4.2x+4.2x +.3

1.8 +.5x = .3

Subtract 1.8 from each side

1.8 +.5x -1.8 = .3 -1.8

.5x = -1.5

Divide each side by .5

.5x/.5 = -1.5/.5

x = -3

Answer:

x=-3

Step-by-step explanation:

In order to solve this equation, we have to isolate x. Perform the opposite of what is being done to the equation. Remember to perform everything to both sides.

1.8-3.7x= -4.2x +0.3

3.7x is being subtracted from 1.8 (-3.7x). The inverse operation of subtraction is addition. Add 3.7x to both sides.

1.8-3.7x+3.7x= -4.2x+3.7x+0.3

1.8= -4.2x+3.7x+0.3

1.8= -0.5x+0.3

0.3 is being added to -0.5x. The opposite of addition is subtraction. Subtract 0.3 from both sides.

1.8-0.3= -0.5x+0.3-0.3

1.8-0.3 = -0.5x

1.5=-0.5x

-0.5 and x are being multiplied (-0.5*x= -0.5x). The opposite of multiplication is division. Divide both sides by -0.5.

1.5/-0.5=-0.5x/-0.5

1.5/-0.5=x

-3=x

Answer:

6 and -2

Step-by-step explanation:

x^2-4x-12

set up equal to zero

x^2-4x-12=0

lets factor:

(x-6)(x+2)=0

x-6=0

x=6

or

x+2=0

x=-2

Answer:

x=6  x=-2

Step-by-step explanation:

x^2-4x-12 = 0

Factor

What two numbers multiply to -12 and add to -4

-6*2 = -12

-6+2 = -4

(x-6)(x+2) =0

Using the zero product property

(x-6) =0   x+2 = 0

x=6  x=-2

Answer:

So if 17/25 of the students like math, science, and art and 3/20 of the students like art only. We first need to find common demoninator. 68/100 and for the second one 15/100. Subtract them both

68-15 = 53/100 of the students factor math, and science or 53%

Answer:

A.

Step-by-step explanation:

Since they are similar, hence taking proportionality,

CA/CB = d1/d2

Cross Multiplying

We get

CA × d2 = CB × d1

OR

d1×CB = d2 × CA

Answer:50%

Step-by-step explanation:670/1340 = 1/2 = 50%

Answer:

1.08

Step-by-step explanation:

If Romeo earns 8% more than Juliet,

Example?

If Juliet earns $80

80x8% = 6.40  So his pay would be 80 + 6.40

If you times 80 by 1.08 (this would also be 108%) you would get $86.40

Use the Pythagorean theorem to solve.

Height = sqrt(12^2 -3^2)

Height = sqrt(144-9)

Height = sqrt(135)

Height = 11.6189 = 11.6 feet

Answer:

The group that has greater value of relative dispersion is the smokers group, as the coefficient of variationof their data is bigger than the coefficient of variation of the non-smokers group data.

CV smokers: 0.387

CV non-smokers: 0.234

Step-by-step explanation:

We will calculate the relative dispersion of each data set with its coefficient of variation (ratio of the standard deviation to the arithmetic mean).

Then, first we calculate the mean and standard deviation for the smokers data:

Mean: 43.7

Standard deviation: 286.5

[tex]M_s=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M_s=\dfrac{1}{12}(69.3+56+22.1+47.6+53.2+. . .+13.8)\\\\\\M_s=\dfrac{524.4}{12}\\\\\\M_s=43.7\\\\\\s_s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M_s)^2\\\\\\s_s=\dfrac{1}{11}((69.3-43.7)^2+. . . +(13.8-43.7)^2)\\\\\\s_s=\dfrac{3152}{11}\\\\\\s_s=286.5\\\\\\[/tex]

The mean and standard deviation for the non-smokers is:

Mean: 30.3

Standard deviation: 50.9

[tex]M_n=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M_n=\dfrac{1}{15}(28.6+25.1+26.4+34.9+28.8+. . .+13.9)\\\\\\M_n=\dfrac{453.8}{15}\\\\\\M_n=30.3\\\\\\s_n=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M_n)^2\\\\\\s_n=\dfrac{1}{14}((28.6-30.3)^2+. . . +(13.9-30.3)^2)\\\\\\s_n=\dfrac{713.3}{14}\\\\\\s_n=50.9\\\\\\[/tex]

Now, we can calculate the coefficient of variation:

CV smokers:

[tex]CV_s=\dfrac{s_s}{M_s}=\dfrac{16.9}{43.7}=0.387[/tex]

CV non-smokers:

[tex]CV_n=\dfrac{s_n}{M_n}=\dfrac{7.1}{30.3}=0.234[/tex]

Answer:

26.94% probability that when he enters the restaurant today it will be at least 5 minutes until he is served.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 4.2, \sigma = 1.3[/tex]

Find the probability that when he enters the restaurant today it will be at least 5 minutes until he is served.

This is 1 subtracted by the pvalue of Z when X = 5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{5 - 4.2}{1.3}[/tex]

[tex]Z = 0.615[/tex]

[tex]Z = 0.615[/tex] has a pvalue of 0.7308.

1 - 0.7308 = 0.2694

26.94% probability that when he enters the restaurant today it will be at least 5 minutes until he is served.

Answer:

10-19 ⇒ 3

50-59 ⇒ 4

Answer:

# of ties    # of racks

 10-19               3

50-59              4

Step-by-step explanation:

Using the Stem and Leaf plot, our data is:

11, 12, 16

21

32, 34, 36, 37, 39

41, 45

51, 52, 53, 56

# of ties    # of racks

 10-19               3 (11, 12, 16)

50-59              4 (51, 52, 53, 56)

Answer:

1.5 meters

Step-by-step explanation:

The formula for the area of a trapezoid is h * (a+b)/2, where a is the first base and b is the second base. Now, we can work backwards to determine the height of the trapezoid:

3.75=h*(1.7+3.3)/2

3.75=h*2.5

h=3.75/2.5=1.5

Hope this helps!

Answer:

Step-by-step explanation:

use the formula and rearrange for h.

1/2 x h x  (a + b) = A

1/2 x (1.7 + 3.3) x h = 3.75

2.5 x h = 3.75

h = 1.5

hope this helps! :)

Answer:

Step-by-step explanation:

Corresponding true average energy expenditure of shovel with conventional blade and true average energy expenditure of shovel with perforated blades form matched pairs.

The data for the test are the differences between the true average energy expenditures of the shovels.

μd = true average energy expenditure of shovel with conventional blade minus true average energy expenditure of shovel with perforated blades.

Conventional perforated diff

0.0011 0.0011 0

0.0014 0.0010 0.0004

0.0018 0.0019 -0.0001

0.0022 0.0013 0.0009

0.0010 0.0011 -0.0001

0.0016 0.0017 -0.0001

0.0028 0.0024 0.0004

0.0020 0.002 0

0.0015 0.0013 0.0002

0.0023 0.0017 0.0006

0.0017 0.002 -0.0003

0.0020 0.0013 0.0007

0.0014 0.0013 0.0001

Sample mean, xd

= (0 + 0.0004 - 0.0001 + 0.0009 - 0.0001 - 0.0001 + 0.0004 + 0 + 0.0002 + 0.0006 - 0.0003 + 0.0007 + 0.0001)/13 = 0.0002077

xd = 0.0002077

Standard deviation = √(summation(x - mean)²/n

n = 13

Summation(x - mean)² = (0 - 0.0002077)^2 + (0.0004 - 0.0002077)^2 + (- 0.0001 - 0.0002077)^2+ (0.0009 - 0.0002077)^2 + (- 0.0001 - 0.0002077)^2 + ( - 0.0001 - 0.0002077)^2 + (0.0004 - 0.0002077)^2 + (0 - 0.0002077)^2 + (0.0002 - 0.0002077)^2 + (0.0006 - 0.0002077)^2 + (- 0.0003 - 0.0002077)^2 + (0.0007 - 0.0002077)^2 + (0.0001 - 0.0002077)^2 = 0.00000158923

Standard deviation = √(0.00000158923/13

sd = 0.00035

For the null hypothesis

H0: μd ≥ 0

For the alternative hypothesis

H1: μd < 0

The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 13 - 1 = 12

The formula for determining the test statistic is

t = (xd - μd)/(sd/√n)

t = (0.0002077 - 0)/(0.00035/√13)

t = 2.14

We would determine the probability value by using the t test calculator.

p = 0.027

Since alpha, 0.05 > than the p value, 0.027, then we would reject the null hypothesis. Therefore, at 5% significance level, we can conclude that the true average energy expenditure using the conventional shovel does not exceed that using the perforated shovel.

Answer:

Step-by-step explanation:

We can let x represent the width. Then the length will be represented by (3x+5), a value 5 more than 3 times the width.

The area is the product of length and width, so is ...

  A = (3x +5)(x) = 3x^2 +5x

To make the area 350, we can find the value of x from ...

  3x^2 +5x = 350

This can be solved a number of ways. One of them is "completing the square".

  3(x^2 +5/3x) = 350

We choose to divide by 3 and add the square of half the x-coefficient.

  x^2 +5/3x +(5/6)^2 = (350/3) + (5/6)^2

  (x +5/6)^2 = 4225/36 . . . . simplify

  x +5/6 = ±√(4225/36) = ±10 5/6 . . . . take the square root

  x = 10  or  -11 2/3 . . . . subtract 5/6

The positive solution is the one of interest: x = 10.

The driveway is 10 ft wide and 35 ft long.

Answer:

4. 27

Step-by-step explanation:

11-10=1 which is <=16

15-10=5 which is <=16

26-10=16 which is <=16

27-10=17 which isn't <=16

Therefore 27 doesn't satisfy the inequality

Answer:

4.   27

Step-by-step explanation:

w - 10 ≤ 16

w≤16 + 10

w ≤ 26

11 ≤ 26

15≤26

26≤26

26≤ 27 False

Answer:

Step-by-step explanation:

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

Where

x1 = sample mean of type A paint

x2 = sample mean of type B paint

s1 = sample standard deviation type A paint

s2 = sample standard for type B paint

n1 = number of samples of type A paint

n2 = number of samples of type B paint

From the information given,

x1 = 75.7

s1 = 4.5

n1 = 11

x2 = 64.3

s2 = 5.1

n2 = 9

x1 - x2 = 75.7 - 64.3 = 11.4

√(s1²/n1 + s2²/n2) = √(4.5²/11 + 5.1²/9) = √4.709

Degree of freedom = (n1 - 1) + (n2 - 1)

df = (11 - 1) + (9 - 1) = 18

For the 98% confidence interval, the z score from the t distribution table is 2.552

Margin of error = 2.552√4.709 = 5.55

The upper boundary for the confidence interval is

11.4 + 5.55 = 16.95 hours

The lower boundary for the confidence interval is

11.4 - 5.55 = 5.85 hours

The correct option is

B. 5.85 hrs < μ1 - μ2 < 16.95 hrs

Answer:

Terrance is 25.5

Step-by-step explanation:

Answer:

Hello There. The correct answer is 26

T = 3.5 + 22.5 = 26

Hope It Helps!

Answer:

Step-by-step explanation:

24/3 - 4

8 - 4 = 4

Answer:

2

Step-by-step explanation:

as you can see the slope of the line y = -1/2x + 5 is -1/2

the slope m of any line perpendicular to it should verify : -1/2×m = -1

-1/2×m = -1

→ multiply both sides by -2

m = 2

Answer:

its b I belive

Step-by-step explanation:

Answer:

The answer is B.

Step-by-step explanation:

In order to find (f-g)(x), you have to subtract g(x) from f(x) :

[tex]f(x) = {3}^{x} + 10[/tex]

[tex]g(x) = 2x - 4[/tex]

[tex](f - g)(x) = {3}^{x} + 10 - 2x - ( - 4)[/tex]

[tex](f - g)(x) = {3}^{x} + 10 - 2x + 4[/tex]

[tex](f - g)(x) = {3}^{x} - 2x + 14[/tex]

Answer:

B:

Step-by-step explanation:

Measure of ARC AFB is 180°

Why?

This is because AB is a diameter.

Answer:

x=-21

Step-by-step explanation:

x+12=-9

minus twelve on both sides

-9-12 equals -21

x=-21