Answer:
The surface area of Design A is smaller than the surface area of Design B.
The area of Design A is 94.65% of the Design B.
Step-by-step explanation:
The area of a right cone is given by the sum of the circle area of the base and the lateral area:
[tex] A = \pi r^{2} + \pi rL [/tex] (1)
Where:
r: is the radius
L: is the slant height
The slant height is related to the height and to the radius by Pitagoras:
[tex] L^{2} = H^{2} + r^{2} [/tex]
[tex] L = \sqrt{H^{2} + r^{2}} [/tex] (2)
By entering equation (2) into (1) we have:
[tex] A = \pi r^{2} + \pi r(\sqrt{H^{2} + r^{2}}) [/tex]
Now, let's find the area of the two cases.
Design A: height that is double the diameter of the base, H= 2D = 4r
[tex] A_{1} = \pi r^{2} + \pi r(\sqrt{(4r)^{2} + r^{2}}) = \pi r^{2}(1+ \sqrt{17}) [/tex]
The volume of the cone is:
[tex]V = \frac{1}{3}\pi r^{2}H[/tex]
We can find "r":
[tex] V = \frac{1}{3}\pi r^{2}(4r) = \frac{4}{3}\pi r^{3} [/tex]
[tex] r = \sqrt[3]{\frac{3V}{4\pi}} = \sqrt[3]{\frac{3*1000}{4\pi}} = 6.20 cm [/tex]
The area is:
[tex] A_{1} = \pi (6.20)^{2}(1+ \sqrt{17}) = 618.7 cm^{2} [/tex]
Design B: height that is triple the diameter of the base, H = 3D = 6r
The radius is:
[tex] r = \sqrt[3]{\frac{3V}{6\pi}} = \sqrt[3]{\frac{3*1000}{6\pi}} = 5.42 cm [/tex]
The area is:
[tex]A_{2} = \pi r^{2} + \pi r(\sqrt{(6r)^{2} + r^{2}}) = \pi r^{2}(1 + \sqrt{37}) = \pi (5.42)^{2}(1 + \sqrt{37}) = 653.7 cm^{2}[/tex]
Hence, the surface area of Design A is smaller than the surface area of Design B.
The percent of the surface area of Design A is less than Design B by:
[tex] \% A = \frac{618.7 cm^{2}}{653.7 cm^{2}}\times 100 = 94.65 \% [/tex]
Therefore, the area of Design A is 94.65% of the Design B.
I hope it helps you!
PLEASE HELP ILL GIVE BRAINLIEST ASAP
Answer:
Jody has to pay $14.24 for total after splitting the tip amount with Karen.
Hope this helps!!!!!
Which budget categories are both variable expenses?
Answer:Utilities and Groceries
Step-by-step explanation:Variable expenses are defined as such because the amount you spend may vary each month. Although variable costs are quite often discretionary expenses, some may be necessities. Buying gas for your car each month is a variable expense, as are car repairs and maintenance. Grocery shopping is also a variable expense.
Answer:
d
Step-by-step explanation:
1 2/3 + 1 1/2 what is the answerrrrrrrrr
Hi!
[tex]1 \frac{2}{3} + 1 \frac{1}{2} = 1 \frac{4}{6} + 1 \frac{3}{6} = 2 \frac{7}{6} = 3 \frac{1}{6} [/tex]
Greetings!
Which of the following shapes is the base of a cone?
O A. Circle
O B. Pentagon
O C. Triangle
OD. Square
The shapes is the base of a cone is Circle.
What is Circle?A circle is often referred to as the locus of points drawn equidistant from the centre. The radius of a circle is the distance between its centre and its outer line. The diameter of a circle is the line that divides it into two equal sections and is equal to twice the radius.
A circle is a fundamental 2D form that is measured by its radius.
We have a Cone.
A Cone if compared as two dimensional then a cone have have Triangular shape.
and, the base of cone have a circular shape.
Thus, the shape of base of cone is Circle.
Learn more about Circle here:
https://brainly.com/question/29142813
#SPJ5
What is mZD? *
B
50°
F
250
Ε
650
А.
Answer:
[tex] m\angle D = 40\degree[/tex]
Step-by-step explanation:
[tex] m\angle DEC = 25\degree [/tex]
(Vertical angles)
[tex] m\angle DCE = 180\degree - 65\degree [/tex]
(Linear pair angles)
[tex] m\angle DCE = 115\degree [/tex]
In [tex] \triangle DCE[/tex]
By interior angle sum postulate of a triangle
[tex] m\angle D = 180\degree-(115\degree + 25\degree) [/tex]
[tex] m\angle D = 180\degree-140\degree[/tex]
[tex] m\angle D = 40\degree[/tex]
After 2 hours, the air temperature had risen 7° f. How long will it take at this rate for the temperature to rise an additional 13°f?
Answer:
21 hours
Step-by-step explanation:
After 2 hours the temperature has risen to 7°f
The time taken to rise to an additional 13°f can be calculated as follows
1 hour takes 3.5°f
13°f = 3.5×6
= 21 hours
Hence it would take 21 hours
Write a congruence statement for the angles and/or sides that are given. State what additional information is required in order to know what the triangle are congruent for the given reason. WILL MARK BRIANLIEST !!!!!!!!! HELPP !!!
Step-by-step explanation:
Required information to prove the triangles are congruent:
AB=FE
Then you can say they are congruent by SAS
What are the angle measures of the triangle?
A. 30°, 60°, and 90°
B. 45°, 45° and 90°
C. 60°, 60°, and 60°
D. They cannot be determined.
what graph is y=1/2x+3 y=3/2x-1
Some one please answer this for me I need it rn and I need an answer not a link
Answer:
B
Step-by-step explanation:
Answer:
maybe just multiply them
then add all oh the options and find there answer if the answer of any of the option matches that's your answer
have a nice day
#Captainpower
List five numbers that have 3, 5, and 11 as prime factors
Answer:
11 1,11 1 x 11
13 1, 13 1 x 13
17 1, 17 1 x 17
19 1, 19 1 x 19
Step-by-step explanation:
evaluate 2^-4
a. -8
b.-16
c.1/8
d.1/16
Answer:
DD
Step-by-step explanation:
Find the perimeter of the rectangle
I don’t understand this someone explain
Answer:
38cm
Step-by-step explanation:
12.6 x 2= 25.2
6.4 x 2= 12.8
25.2 + 12.8= 38
HELP 87 points if you do
Answer:
it's on the picture hope you are doing well
Step-by-step explanation:
hope it helps make brainlliest ty
Solve for X LT1 10th grade level
Answer:
3
Step-by-step explanation:
The triangles are similar, therefore :
2.4/4 = 1.8/x
x = 18 × 4/24 = 3
what is y=36^2 x 49
HELP MEEEEEEEEE!!!!!!!!
Answer: y=36^(2)x*49
Step-by-step explanation: Graph.
Brainliest or a thank you if im right please :)) <3
Find the equation of the line of the graph
Answer:
So this is a negative slope remember this. We are going to use y = mx + b
m is the slope b is the y intercept. In this problem, the y intercept is 6.
The slope is -2;
Y = -2x + 6
Step-by-step explanation:
If 5^a =625, then find the value of a.
Answer:
a = 4
Step-by-step explanation:
note that 625 = [tex]5^{4}[/tex] , then
[tex]5^{a}[/tex] = [tex]5^{4}[/tex]
Since the bases on both sides are equal, both 5 then equate exponents, so
a = 4
Answer:
4
Step-by-step explanation:
Prime factorize 625
625 = 25 * 25 = 5 * 5 * 5 * 5
[tex]5^{a} = 625\\\\5^{a} = 5^{4}[/tex]
As base are same, compare the exponents
a = 4
Can someone help me on this plzzz and thank you
Answer:
-1.5
Step-by-step explanation:
5x6=30
30-21=9
9/6=1.5
remember tht the answer is NEGATIVE,, thnk u hav a good nite
In Juan's coin bank there are nickels (n),
dimes (d), and quarters (q). The number of
quarters is one-quarter the number of dimes, and
the number of nickels is twice the number of
quarters. The total value of the coins is $6.00.
Find the number of each type of coin. [Show all
work.]
Answer:
The answer is 8 quarters, 16 nickles, and 32 dimes
Step-by-step explanation:
First, the equation would be (2/4d) x 5 +d x 10 +1/4d x 25= 600 (Don't put 6.00, that's dollars. We put 6 dollars into cents to make it easier.) Then we slowly start to solve: 10/4d + 10d + 25/4d = 600 10d+40d+25d/4 = 600 (Put all of that over 4, not first 25d) 75d= 600 x 4 d=600 x 4/75 (same here put everything over 75) d=32 So then n= 2 x 32/4 = 16 Then n would be equal to : 1/4d= 1/4 x 32 = 8 So your answer would be 8 quarters, 16 nickles, and 32 dimes.Hope this helped :)
1. Alex bought 2 buckets of baseballs that cost $19.49 each, a bat that cost $125.50, and 2 pair of baseball socks that totaled $29.50. The tax on Alex's purchases equaled $16. How much change did Alex receive if he paid with three $100 bills?
Answer:
$90.02
Step-by-step explanation:
Solve
Formula: Change money = paid money – bill. Paid money = change + bill.
Given: 2 buckets of baseballs that cost $19.49 each
A bat that cost $125.50, and 2 pairs of baseball socks that totaled $29.50
Tax on Alex's purchases equaled $16.
Paid with three $100 bills.
To find: How much change Alex received if he paid with three $100 bills
Total payment + Total Tax -Total cost
19.49 + 125.50 + 29.50 = 174.49 (Don't add the $16 tax because that will be taken from the amount we pay)
∴, three 100 bills is 300
So, 300 - 174.49 = 109.51
109.51 - 16 = 90.51
90.51 - 0.49 = $90.02
A scale model of a building is 8 inches tall. The actual building is 120 feet tall. What is the scale factor of the model? (1ft. = 12 in.)
Answer:
1:180
Step-by-step explanation:
We start by multiplying the 120 feet by 12 inches to get the height of the building in inches, which is 1440.
Then, we have a ratio of 8:1440, which simplifies to 1:180 when we divide 1440 by 8.
The required scale factor of the given model is 1/180.
What is a scale image?Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object.
A building scale model is 8 inches tall. The original structure stands 120 feet tall.
Here 1 foot is equal to twelve inches which is given in the question.
As per the given situation, the required solution would be as :
Firstly we have to multiply 120 feet by 12 inches to obtain the building's height in inches, which is 1440.
The result is an 8/1440 ratio, which simplifies to 1/180 when 1440 is divided by 8.
Therefore, the required scale factor of the given model is 1/180.
Learn more about the Scale images here:
brainly.com/question/13194929
#SPJ2
help me please i will really appreciate it
Answer:
2.H
Step-by-step explanation:
please click the heart and rate excellent and brainleist to
A filter in the shape of a cone has a diameter of 3 inches and a height of 4 inches.
How much liquid can the filter hold without it overflowing?
A.
B.
C.
D.
Answer:
9.42 cubic inches
Step-by-step explanation:
We are to find the volume of the cone.
The formula is given as:
1/3πr²h
From the question,
Diameter = 3 inches, Radius = D/2 = 3/2
r = 1.5 inches
h = 4 inches
Hence, the volume of the cone =
1/3 × π × 1.5² × 4
= 9.42 cubic inches
Therefore, the filter can hold 9.42 cubic inches of liquid without overflowing.
I NEED HELP ASAP PLEASE
Answer: x = 8.3334
Step-by-step explanation:
assuming im solving for x ??
(6x + 8) + (19x - 3) = 180
21x + 5 = 180
- 5 - 5
21x = 175
/ 21 / 21
x = 8.3334
What two numbers have a product of 16 and a sum of 8?
Cuantas cajas de gelatina con volumen de 500cm cúbicos caben en una caja de 1m cúbico?
Answer:
2000 cajas de gelatina.
Step-by-step explanation:
Answer:
2000 cajas de gelatina.
Step-by-step explanation:
1 m^3 : 1 000 000 cm^3
Hallamos las cajas de gelatina :
1 000 000 cm^3 / 500cm^3 = 2000
Respuesta : 2000 cajas de gelatina.
what are the first four terms of the sequence an=n2+4
Step-by-step explanation:
Given formula
an = n² + 4
Now the first four terms of the sequence are
a1 = 1² + 4 = 5
a2 = 2² + 4 = 4 + 4 = 8
a3 = 3² + 4 = 9 + 4 = 13
a4 = 4² + 4 = 16 + 4 = 20
The terms are
5 , 8 , 13 and 20.
What is the sum of the interior angles of a rectangle?
4°
360°
180°
90°
Answer: 180
The sum of the angles in a rectangle is given by (n-2)180 where n is the number of sides of the polygon and n is greater than or equal to 3. For a rectangle, n=4 thus sum of angles is (4–2)180 = 360 degrees. Each interior angle is 360/4 = 90 degrees.
Answer:
180⁰is the interior angle of a rectangle
pls answer this tyyyyy
Answer:
110 is the answer
Step-by-step explanation:
