the volume of a rectangular prism is 2.5 cubic feet. the prism has a height of 15 inches. what is the area…

the volume of a rectangular prism is 2.5 cubic feet. the prism has a height of 15 inches. what is the area, in square inches, of the base of the prism? unit conversion table 1 ft³ = 1,728 in.³ 1 ft² = 144 in.² 1 ft = 12 in. type the number in the box. square inches

the volume of a rectangular prism is 2.5 cubic feet. the prism has a height of 15 inches. what is the area, in square inches, of the base of the prism? unit conversion table 1 ft³ = 1,728 in.³ 1 ft² = 144 in.² 1 ft = 12 in. type the number in the box. square inches

Answer

Explanation:

Step1: Convert volume to cubic - inches

Since (1\ ft^{3}=1728\ in^{3}), and the volume (V = 2.5\ ft^{3}), then (V=2.5\times1728\ in^{3}=4320\ in^{3}).

Step2: Use the volume formula for a rectangular prism

The volume formula of a rectangular prism is (V = Bh), where (B) is the area of the base and (h) is the height. Given (h = 15) inches and (V = 4320\ in^{3}), we can solve for (B) by (B=\frac{V}{h}).

Step3: Calculate the base - area

(B=\frac{4320}{15}=288) square inches.

Answer:

288