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.

Question

3 years ago

7

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

1 answer:

EleoNora [17] · Answer 1 · 2022-06-04T01:28:13+03:00

Answer:

927 cubic inches

Step-by-step 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.