Question Video: Calculating the Volume of a Square-Based Pyramid | Nagwa Question Video: Calculating the Volume of a Square-Based Pyramid | Nagwa

# Question Video: Calculating the Volume of a Square-Based Pyramid Mathematics

Work out the volume of a square-based pyramid with a height of 12 inches and a base length of 5 inches.

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### Video Transcript

Work out the volume of a square-based pyramid with a height of 12 inches and a base length of five inches.

Let’s begin this question by sketching a diagram of this pyramid. As we’re told that this pyramid has a base length of five inches, since this is a square, we know that both the length and the width will be the same. The height of 12 inches refers to the perpendicular height of the pyramid. We can recall that the volume of a pyramid is equal to a third multiplied by the area of the base multiplied by the height.

So, to find the area of the base, which is a square in this case, we know that that will be the length multiplied by the length. So, that’s five times five, giving us 25 square inches. So, to find the volume of the pyramid, we take the area of our base, which is 25. So, we have a third times 25 times the height, which is 12 inches. We can simplify this calculation by finding a third of 12, which is four. So, we now have the calculation 25 multiplied by four, which is 100. And our units here will be cubic inches. So, our final answer for the volume of the pyramid is 100 cubic inches.

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