Question Video: Finding the Volume of a Pyramid given Its Height and Its Base Side Lengths | Nagwa Question Video: Finding the Volume of a Pyramid given Its Height and Its Base Side Lengths | Nagwa

# Question Video: Finding the Volume of a Pyramid given Its Height and Its Base Side Lengths Mathematics • Second Year of Secondary School

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Determine, to the nearest hundredth, the volume of the pyramid.

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### Video Transcript

Determine, to the nearest hundredth, the volume of the shown pyramid.

In order to answer this question, we can recall that to find the volume of a pyramid, we calculate one-third times the area of the base times the perpendicular height. In order to use this formula, although we are given the perpendicular height as nine meters, we’re not given the area of the base, so we’ll need to calculate it. Because the base is a triangle, we’ll use the formula to find the area of a triangle, which is a half times the base times the height. Notice that with these two formulas, we use the height twice, but it’s not the same height. For the area of a triangle, the height is the height of the triangle and for the height in the volume formula, that’s the height of the pyramid.

So, let’s work out the area of the triangle. So, we can take six as the base and 4.7 as the height, and we can use 4.7 directly because we’re given that this is a perpendicular height. When we work out this calculation, we get an answer of 14.1. Now, remember that this is an area and the units we’re given are in meters, so our area will be in meters squared. We can now use this value to calculate the volume of a pyramid, filling in the value that the area of the base is 14.1 and the height of the pyramid this time is nine meters. When we calculate one-third times 14.1 times nine, we get an answer of 42.3. And as this is a volume, we’ll have cubic units, so we’ll have a value of meters cubed. We can indicate the answer to the nearest hundredth by adding a zero in the hundredths column to give us the volume as 42.30 cubic meters.

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