A solid rectangular block has a square base with an area of 25 square inches. If the total… — Armed Services Vocational Aptitude Battery (ASVAB)

A solid rectangular block has a square base with an area of $25$ square inches. If the total volume of the block is $150$ cubic inches, what is the total surface area of the block in square inches?

A
$150$
B
$200$
$170$ Answer
D
$220$

Answer

170

To find the total surface area, all dimensions of the block must be known. The side length of the square base is

\sqrt{25} = 5

inches. The height is the volume divided by the base area:

150 \div 25 = 6

inches. The total surface area is the sum of the areas of all six faces: two square bases (

2 \times 25 = 50

) and four identical rectangular sides (

4 \times 5 \times 6 = 120

). The total is

50 + 120 = 170

square inches.

Step-by-Step Solution

Find the side length of the square base.

5

inches

The area of a square is the side length squared (

s^2 = 25

), so the side length is the square root of the area.

Find the height of the rectangular block.

6

inches

The volume of a rectangular block is the base area multiplied by the height (

V = B \times h

). Dividing the volume (

150

) by the base area (

25

) gives the height.

Calculate the total surface area of the block.

170

square inches

The total surface area is the sum of the two square bases (

2 \times 25 = 50

) and the four identical rectangular sides (

4 \times 5 \times 6 = 120

). Adding these together yields

50 + 120 = 170

Key Concept

Volume and Surface Area of Rectangular Prisms

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