This diagram shows the dimensions of a concrete piece used to build a deck.

What is the volume of the concrete piece?






Three-dimensional figure that could be formed by placing two rectangular prisms together to form an L shape where the longer part of the L is on the bottom and the shorter part of the L extends up from the left side. The longer part of the L has a length of 20 inches, a width of 9 inches, and a height of 9 inches. The shorter part of the L extends 10 inches above the longer part of the L and has a length of 5 inches.

Answer:

The student is wrong, the total area = 16 ft² + 20 ft²

Step-by-step explanation:

See the attached figure.

The shown figure is a composite area of:

1) A rectangle with length of 8 ft and width of 4 ft

2) A triangle of base (8 - 4 = 4ft) and height of ( 6 - 4 = 2 ft)

The area of the rectangle = length x width = 8 * 4 = 32 ft²

The area of the triangle = 0.5 base x height = 0.5 * 4 * 2 = 4 ft²

So, the total area = 32 + 4 = 36 ft²

OR

The figure can be consists of :

1) A square of side length of 4 ft

2) A trapezoid of height (8-4 = 4 ft) and the bases length is (6 and 4 ft)

So,

The area of the square = 4 * 4 = 16 ft²

The area of the trapezoid = 0.5 (6+4) * 4 = 5 * 4 = 20 ft²

So ,the total area = 16 + 20 = 36 ft²

So,

The student is distracted, he finds the area of total rectangle of sides 8 and 6 ft, he should subtract from it the area of the trapezoid of height 2 ft and bases of 4 and 8 ft

So, the student is wrong

The volume of the concrete piece is 1000 cubic inches.

Volume is a measure of the amount of space that an object occupies. It is a three-dimensional measurement that is typically expressed in cubic units.

here, we have,

given that,

The given diagram shows a rectangular concrete piece with dimensions 5 inches, 10 inches, and 20 inches.

The volume of a rectangular prism can be calculated as:

V = l × w × h

Where "l" is the length, "w" is the width, and "h" is the height. So, for the concrete piece, the volume is:

V = 5 in. × 10 in. × 20 in.

  = 1000 cubic inches.

Hence, the volume of the concrete piece is 1000 cubic inches.

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