Question

"A rectangular prism has a height of 3 inches and a volume of 27 cubic inches. The height of this prism is changed to 6 inches, and the other dimensions stay the same. What is the volume of the prism with this change?"

Answer 1

Answer:

$\text{Volume of prism with change}=54\text{ in}^3$

Step-by-step explanation:

We have been given that a rectangular prism has a height of 3 inches and a volume of 27 cubic inches.

We know that volume of rectangular prism is length times width times height.

$V=lwh$

$27\text{ in}^3=lw\cdot 3\text{ in}$

$\frac{27\text{ in}^3}{3\text{ in}}=\frac{lw\cdot 3\text{ in}}{3\text{ in}}$

$9\text{ in}^2=lw$

Since height of the prism is changed to 6 inches and other dimensions stay the same, so volume of prism with change would be 6 times product of length and width.

$\text{Volume of prism with change}=9\text{ in}^2\times 6\text{ in}$

$\text{Volume of prism with change}=54\text{ in}^3$

Therefore, the volume of prism with change would be 54 cubic inches.