Question

15) If a square prism has a volume of 104 cubic centimeters and a height of eight centimeters, explain how to

find the area of the side that is a square.

Answer 1

141 cm^2

Explanation:

Given: V = 104 cm3, h = 8 cm

Since V = Bh, where B is the area of the base, and h is the height of a prism, then

B = V/h substitute the given values:

B = 104 cm3/8 cm

B = 13 cm2, which tells us that the long side of the square base equals the square root of 13.

The surface area of a prism = L.A. + 2B, where L.A. is the lateral area of the prism.

L.A. = pH, where p is the perimeter of the base.

Since p = 4(square root of 13) cm, h = 8cm, and B = 13 cm2, we have:

Surface Area = pH + 2B = [4(square root of 13) cm](8 cm) + 2(13 cm2) = 115.38 cm2 + 26 cm2 = 141 cm2

Thus, the surface area of the prism is approximately 141 cm2.