Video: Finding the Volume of a Right Square Pyramid given Its Height and Its Base Side Length

Find the volume of a right square pyramid whose height is 45 cm and base side length is 25 cm.

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Video Transcript

Find the volume of a right square pyramid whose height is 45 centimetres and base side length is 25 centimetres.

So we know that we have a pyramid, which means it will come up to a peak — a point. And it’s a square pyramid. So the base will be a square. And it’s a right square pyramid. So the height will be perpendicular to the base. So let’s begin by drawing the pyramid itself.

So here, we’ve drawn the right square pyramid. And we need to label the height, which is perpendicular to the base. So here would be our height and we’re drawing a 90-degree angle at the bottom because it’s perpendicular to the base. And it’s 45 centimetres. And now, we need to label the base side length of 25 centimetres. But in a square, all sides are equal. So we can label them all 25 centimetres.

And now, we can begin solving for the volume. The volume of a pyramid is equal to one-third times capital 𝐵 times ℎ, where capital 𝐵 is equal to the area of the base. And here our base is a square. So the area of the base will be length times width, which since the length and the width are the same thing, it could be side times side, which is the same thing as side squared. It will be 25 centimetres times 25 centimetres. So the area of the base will be 625 centimetres squared.

So right now, we have one-third times 625 centimetres squared times the height. So now, we need to plug in the height of the right square pyramid, which we know to be 45 centimetres. And now, we multiply to get a final answer of 9375 centimetres cubed, which may also be said or pronounced as 9375 cubic centimetres.

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