Video Transcript
A cylinder has a volume of 900 cubic centimeters and a base with a diameter of 14
centimeters. Find the height of the cylinder to two decimal places.
We begin by recalling that the volume 𝑉 of a cylinder of radius 𝑟 and height ℎ is
given by the formula 𝑉 is equal to 𝜋𝑟 squared ℎ. In this question, we are given a volume 𝑉 equal to 900 cubic centimeters and a
diameter of 14 centimeters. And we need to use this information to calculate the height. Before we can apply the formula, we must work out the radius of the cylinder, which
is half the length of the diameter. One-half of 14 centimeters equals seven centimeters. So, the radius of the cylinder is seven centimeters.
Substituting the values of 𝑉 and 𝑟 into the formula, we have 900 equals 𝜋
multiplied by seven squared multiplied by ℎ. Since seven squared is 49, this simplifies to 900 is equal to 𝜋 multiplied by 49
multiplied by ℎ. Dividing both sides by 𝜋 and 49, we have ℎ is equal to 900 divided by 49𝜋. Typing the left-hand side into the calculator gives us ℎ is equal to 5.8465 and so
on. We are asked to round our answer to two decimal places, which is 5.85.
We can therefore conclude that the height of the cylinder is 5.85 centimeters to two
decimal places.
