Video Transcript
Given that a square pyramid has a
volume of 372 cubic centimeters and a height of 31 centimeters, determine the
perimeter of its base.
We haven’t been given a diagram
here, but sometimes it can be helpful to sketch one. Firstly, we’re told that this is a
square pyramid, so we’ll know that the length and the width will be exactly the same
measurement on the base. We’re given the volume of the
pyramid as 372 cubic centimeters and we’re given the perpendicular height as 31
centimeters. We can recall that the volume of a
pyramid is equal to one-third times the area of the base times the perpendicular
height. We can use the fact that we are
given the volume of the pyramid and its perpendicular height to find the area of the
base. This will allow us to then
calculate the perimeter of the base.
We can substitute in the values
then. The volume is 372 and the height is
31 to give us 372 is equal to one-third times the area of the base times 31. Multiplying both sides by three, we
have 1116 is equal to the area of the base times 31. Next, we divide both sides by 31 to
give us the area of the base is 36 square centimeters. So, how do we go from knowing the
area of the base of this pyramid to finding its perimeter? Well, remember that the base is a
square. So, if we define the length of one
side as 𝑙, then all the other sides would be of length 𝑙. The area of a square would be
calculated as 𝑙 squared. In this case, 𝑙 squared must have
given us 36. To calculate 𝑙, we would take the
square root of both sides, and the square root of 36 is six. And of course, the length units
will be in centimeters.
To find the perimeter, that’s the
distance around the outside edge. We could add six and six and six
and six or more simply work out six times four, which would give us a value of
24. And because perimeter is still a
length, then we’d have the units of centimeters. And so, we found that the perimeter
of the base of this pyramid is 24 centimeters, and we did that using the volume by
first calculating the area of the base.
