Question

Prism M is a dilation of Prism N. The height of Prism M is 4 3/4 ft, and the volume of Prism M is 68 2/5 ft³. The height of Prism N is 2 3/8 ft. What is the volume of Prism N?Enter your answer as a mixed number in simplest form by filling in the boxes.

Answer 1

The answer is 8 11/20.

Answer 2

8 11/20 ft³

Explanation:

For dilated figures, the ratio of volumes is the cube of the ratio of corresponding linear dimensions.

Vn/Vm = (Hn/Hm)³

Vn = Vm(Hn/Hm)³ = (68 2/5 ft³)((2 3/8 ft)/(4 3/4 ft))³

Vn = (342/5 ft³)((19/8)/(19/4))³ = (342/5 ft³)(1/2)³ = 342/40 ft³

Vn = 8 11/20 ft³

The volume of Prism N is 8 11/20 ft³.