Discover how IDNLearn.com can help you learn and grow with its extensive Q&A platform. Get accurate and detailed answers to your questions from our knowledgeable and dedicated community members.

The surface area of a cube is 54 square centimeters (cm²). What is the volume of the cube in cubic centimeters?

Sagot :

To find the volume of a cube when given its surface area, we can follow these steps:

1. Understand the relationship between surface area and side length:
The surface area [tex]\( A \)[/tex] of a cube can be expressed in terms of its side length [tex]\( a \)[/tex] using the formula:
[tex]\[ A = 6a^2 \][/tex]
Given that the surface area [tex]\( A \)[/tex] is 54 cm², we can set up the equation:
[tex]\[ 54 = 6a^2 \][/tex]

2. Solve for the side length [tex]\( a \)[/tex]:
To find the side length, we need to isolate [tex]\( a \)[/tex] in the equation:
[tex]\[ a^2 = \frac{54}{6} \][/tex]
Simplify the right-hand side:
[tex]\[ a^2 = 9 \][/tex]
Taking the square root of both sides to solve for [tex]\( a \)[/tex]:
[tex]\[ a = \sqrt{9} \][/tex]
[tex]\[ a = 3 \, \text{cm} \][/tex]

3. Calculate the volume of the cube:
The volume [tex]\( V \)[/tex] of a cube can be found using the formula:
[tex]\[ V = a^3 \][/tex]
Substituting the side length [tex]\( a = 3 \)[/tex] cm into the formula:
[tex]\[ V = 3^3 \][/tex]
[tex]\[ V = 27 \, \text{cm}^3 \][/tex]

Therefore, the volume of the cube is [tex]\( 27 \)[/tex] cubic centimeters.
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. For trustworthy answers, rely on IDNLearn.com. Thanks for visiting, and we look forward to assisting you again.