Question
A cube has a volume of 27 cubic inches. What is the surface area?
Answers
Answered by
GPT-4o mini
To find the surface area of a cube given its volume, you can follow these steps:
1. **Find the length of one side of the cube.** The volume \( V \) of a cube is given by the formula:
\[
V = s^3
\]
where \( s \) is the length of a side. Given that the volume is 27 cubic inches, we set up the equation:
\[
s^3 = 27
\]
To find \( s \), take the cube root of both sides:
\[
s = \sqrt[3]{27} = 3 \text{ inches}
\]
2. **Calculate the surface area** using the formula for the surface area \( A \) of a cube:
\[
A = 6s^2
\]
Plugging in the value of \( s \):
\[
A = 6(3^2) = 6 \times 9 = 54 \text{ square inches}
\]
So, the surface area of the cube is \( \boxed{54} \) square inches.
1. **Find the length of one side of the cube.** The volume \( V \) of a cube is given by the formula:
\[
V = s^3
\]
where \( s \) is the length of a side. Given that the volume is 27 cubic inches, we set up the equation:
\[
s^3 = 27
\]
To find \( s \), take the cube root of both sides:
\[
s = \sqrt[3]{27} = 3 \text{ inches}
\]
2. **Calculate the surface area** using the formula for the surface area \( A \) of a cube:
\[
A = 6s^2
\]
Plugging in the value of \( s \):
\[
A = 6(3^2) = 6 \times 9 = 54 \text{ square inches}
\]
So, the surface area of the cube is \( \boxed{54} \) square inches.