Question

A right prism has a base in the shape of an octagon. The side length of the octagon is 4 inches. The length of the apothem is 4.83 inches. The height of the prism is 12 inches. What is the volume of the prism? Round your answer to the nearest whole number. cubic inches

Answer 1

the answer on edg is 927

Answer 2

927 cubic inches

Explanation:

The area of the octagonal base is ...

A = (1/2)Pa

where P is the perimeter, and 'a' is the apothem. Using the given numbers, the base area is ...

A = (1/2)(8·4)(4.83) = 77.28 . . . square inches

The volume of the prism is given by ...

V = Bh

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

V = (77.28 in^2)(12 in) = 927.36 in^3

The volume of the prism is about 927 cubic inches.