Chapter 9.3, Problem 36PPS

To determine

To find: Area of square and volume of cube if the side length is doubled and tripled.

Answer to Problem 36PPS

When side is doubled then the area of square is $4s^2$ and the volume of cube is $8s^3$.

When the side is tripled then the area is $9s^2$ and the volume is $27s^3$ .

Explanation of Solution

Given information:

As mentioned in the problem side length is $2s$ and the side length is $3s$ .

Formula used:

Area of square $={\left(side\right)}^2$ and volume of cube $={\left(side\right)}^3$ .

Calculation:

Consider the side length as $2s$ and side length as $3s$ .

Case $-1$ :- when side length is doubled that is $2s$ .

Recall that Area of square $={\left(side\right)}^2$ and volume of cube $={\left(side\right)}^3$ .

Therefore area of square is $4s^2$ and volume of cube is $8s^3$ .

Case $-2$ :- when side length is tripled that is $3s$ .

Recall that Area of square $={\left(side\right)}^2$ and volume of cube $={\left(side\right)}^3$ .

Therefore area of square is $9s^2$ and volume of cube is $27s^3$ .

Therefore the area of square is half of volume of cube when side is doubled and area of square is three times of volume when side is triple.