A prism with a base area of 3 m2 and a height of 4 m is dilated by a factor of 3/2 What is the volume of the dilated prism? Enter your answer, as a decimal, in the box. х

Question

asked Mar 28, 2021 168k views

1 Answer

LDMJoe · Answer 1 · 2021-04-02T16:19:48+0000

Answer:

The value of the new volume 'x' would be equal to 40.5 cm³.

Explanation:

Given

We can determine the volume of the original prism by multiplying the area of the base by the height,

volume = (3 cm²)(4 cm) = 12 cm³

Dilation by a factor of 3/2 means that the dimensions of the new prism is 3/2 times that of the original object.

let 'x' be the volume of the new solid,

$(x)/(12)=\left((3)/(2)\right)^3$

(x)/(12)=(27)/(8)

Multiply both sides by 12

$(12x)/(12)=(27\cdot \:12)/(8)$

x=(81)/(2)

x=40.5 cm³

Therefore, the value of the new volume 'x' would be equal to 40.5 cm³.