if the volume of a cube is 125 cubic feet, what will happen to the volume is each side is increased by 5 feet

Answer 1

To find the new volume of the cube after increasing each side by 5 feet, we first need to determine the length of a side of the original cube.

The volume \( V \) of a cube is given by the formula:

\[ V = s^3 \]

where \( s \) is the length of a side of the cube. Given that the volume is 125 cubic feet, we can set up the equation:

\[ s^3 = 125 \]

To find \( s \), we take the cube root of both sides:

\[ s = \sqrt[3]{125} = 5 \text{ feet} \]

Now, we increase each side by 5 feet:

\[ s_{\text{new}} = s + 5 = 5 + 5 = 10 \text{ feet} \]

Next, we calculate the new volume \( V_{\text{new}} \) using the new side length:

\[ V_{\text{new}} = (s_{\text{new}})^3 = (10 \text{ feet})^3 = 1000 \text{ cubic feet} \]

Thus, after increasing each side of the cube by 5 feet, the new volume becomes 1000 cubic feet.

Answer 2

what will the volume increase by?

Answer 3

To find the increase in volume, we can subtract the original volume from the new volume.

The original volume of the cube is 125 cubic feet, and the new volume after increasing each side by 5 feet is 1000 cubic feet.

Volume increase:

\[ \text{Volume increase} = V_{\text{new}} - V_{\text{original}} = 1000 \text{ cubic feet} - 125 \text{ cubic feet} \]

\[ \text{Volume increase} = 875 \text{ cubic feet} \]

Thus, the volume will increase by 875 cubic feet.

Answer 4

how many times greater?

Answer 5

To determine how many times greater the new volume is compared to the original volume, you can divide the new volume by the original volume.

Given:

• Original volume (\( V_{\text{original}} \)) = 125 cubic feet
• New volume (\( V_{\text{new}} \)) = 1000 cubic feet

Calculating the ratio:

\[ \text{Times greater} = \frac{V_{\text{new}}}{V_{\text{original}}} = \frac{1000 \text{ cubic feet}}{125 \text{ cubic feet}} \]

\[ \text{Times greater} = 8 \]

So, the new volume is 8 times greater than the original volume.