The base of a basketball goal has the shape of a rectangular pyramid. The base of the goal must be filled with sand so the goal does not fall down. The base of the pyramid is 4.5 feet long and 4 feet wide. The height of the pyramid is 2.5 feet. How much sand will be needed to fill the base of the basketball goal?

A. 7.1 ft^3

B. 15 ft^3

C. 22.5 ft^3

D. 45 ft^3

Question

Mathematics

Lee Herrera

31 August, 05:59

The base of a basketball goal has the shape of a rectangular pyramid. The base of the goal must be filled with sand so the goal does not fall down. The base of the pyramid is 4.5 feet long and 4 feet wide. The height of the pyramid is 2.5 feet. How much sand will be needed to fill the base of the basketball goal?

A. 7.1 ft^3

B. 15 ft^3

C. 22.5 ft^3

D. 45 ft^3

+2

Answers (1)

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Yasmine Page · Answer 1

B. 15 ft^3

Step-by-step explanation:

The volume of a pyramid is given by the formula ...

V = (1/3) Bh

where B represents the area of the base, and h represents the height.

The base is apparently a rectangle, so its area is the product of its length and width:

B = L·W = (4.5 ft) (4 ft) = 18 ft^2

Then the volume is ...

V = (1/3) (18 ft^2) (2.5 ft) = 15 ft^3

15 cubic feet of sand will be needed to fill the base.