Question

A prism with a base area of 3 m2 and a height of 4 m is dilated by a factor of 3/2

Answer 1

Answer:

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

Step-by-step explanation:

Given

• base area = 3 m²

• height = 4m

• Dilation by a factor scale of 3/2.

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,

$\frac{x}{12}=\left(\frac{3}{2}\right)^3$

$\frac{x}{12}=\frac{27}{8}$

Multiply both sides by 12

$\frac{12x}{12}=\frac{27\cdot \:12}{8}$

$x=\frac{81}{2}$

$x=40.5$ cm³

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