Question

A rectangular prism has a base that is 4 m by 6 m and a height of 10 m. If all dimensions are doubled, what happens to the volume? Explain the steps that you take to arrive at your answer.

Answer 1

When the dimensions of a rectangular prism will be doubled, its volume won't only be doubled but it will be 8 times as much.

The original volume of the rectangular prism is LxWxH.

V= LxWxH
V= (6m) (4m) (10m)
V= 240m³

If we double the dimensions, the volume would be

V= 2L x 2W x 2H
V= 2 x 6m x 2 x 4m x 2 x 10m
V= 2 x 2 x 2 x 6m x 4m x 10m
V= 2³ (6m x 4m x 10m)
V= 2³ x 240m³
V = 8 x 240m³
V= 1920 m³

The new volume now is 1,920 m³, which makes the rectangular prism larger than the original.

Answer 2

When we will double the dimension the volume will be increased by 8 times, and the volume will be $1920m^3$

Given information:

The Volume of rectangular prism = l×b×h

The volume of a prism,

$V= L\times B\times H\\V= (6m) (4m) (10m)\\V= 240m^3$

When all the dimensions are doubled, the new volume will be,

$V_1= 2L \times 2B \times 2H\\V_1= 2 \times6 \times2 \times4\times 2 \times10\\V_1= 2 \times2 \times 2 \times 6\times 4\times 10\\V_1= 2^3 (6\times 4\times10)\\V_1=8\times240m^3\\V_1=1920 m^3$

When we will double the dimension the volume will be increased by 8 times, and the volume will be $1920m^3$.

For more details about rectangular prism, refer to the link given below:

https://brainly.com/question/8890154