Video: Finding the Volume of a Cube given Its Base Area

The base of a cube has an area of 16 cm². What is its volume?

02:11

Video Transcript

The base of a cube has an area of 16 centimeters squared. What is its volume?

A cube is a three-dimensional shape, in which all six of its faces are squares. Its volume can be found by multiplying its three dimensions together. As each face is a square, all of the dimensions of the cube are the same. And in this question, we’ll refer to them as 𝑥 centimeters. The volume is therefore equal to 𝑥 multiplied by 𝑥 multiplied by 𝑥 which is equal to 𝑥 cubed.

In order to find the volume of this cube, we need to know its side length 𝑥. We’re told that the area of the base of the cube which is a square is 16 centimeters squared. The area would be found by multiplying the two dimensions of the square together. And so we have the equation 𝑥 multiplied by 𝑥 or 𝑥 squared is equal to 16. We can solve this equation to find the side length of the cube. We need to take the square root of both sides. Given 𝑥 is equal to the square root of sixteen, 𝑥 is therefore equal to four. So the side length of the cube is four centimeters.

Just a quick note about square rooting to solve the equation 𝑥 squared is equal to 16, usually if you need to solve an equation by square rooting, you would need to take the positive and negative square root. So we would have 𝑥 is equal to plus or minus the square root of 16 — plus or minus four. However, in this question, 𝑥 represents a length and therefore it must take the positive value. This is why we only took the positive square root of 16.

Now that we know the side length of the cube, we can substitute it into our formula for the volume in order to calculate it. The volume is equal to four cubed which is 64. Units for volume are cubic units. So in this question that’s centimeters cubed.

The volume of the cube is 64 centimeters cubed.

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