Question Video: Relating the Volume and Surface Area of a Cube | Nagwa Question Video: Relating the Volume and Surface Area of a Cube | Nagwa

Question Video: Relating the Volume and Surface Area of a Cube Mathematics • Second Year of Preparatory School

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What is the surface area of a cube if its volume is 8 cm³?

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Video Transcript

What is the surface area of a cube if its volume is eight cubic centimeters?

We are given the volume of a cube and asked to find its surface area. To answer this question, we need to recall the formula for the volume of a cube, which is length cubed, and the formula for the surface area of a cube, which is six times the length squared. We recall that all dimensions of a cube, including its height, width, and depth, are equal. Therefore, we can label all dimensions as 𝑙 centimeters.

Knowing that the volume is eight, we can set up the equation eight equals 𝑙 cubed. Then, we solve for 𝑙 by taking the cube root of eight. So we get 𝑙 is equal to two. Now that we have the side length of the cube, we can substitute this value for 𝑙 in the surface area equation. Using proper order of operations, we first square two then multiply by six. Hence, the surface area of a cube with a volume of eight cubic centimeters is 24 square centimeters.

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