Video Transcript
Find the diameter of the base of a
cylinder if the lateral surface area is 434𝜋 square centimeters and the height is
31 centimeters.
We’ve been given the lateral
surface area of a cylinder, along with its height, and asked to determine the
diameter of the cylinder’s circular base. Let’s begin by recalling how the
lateral surface area is calculated.
The lateral surface area of a
cylinder is the area of the curved surface that wraps around the cylinder. This surface is a rectangle, with a
length equal to the circumference of the circular base and a width equal to the
height of the cylinder. The area of this surface is
therefore equal to two 𝜋𝑟ℎ. We can substitute the lateral
surface area of 434𝜋 and the height of 31 to give the equation 434𝜋 equals two
𝜋𝑟 multiplied by 31.
Now, as it is the diameter of the
circular base that we’re asked to calculate, and we know that the diameter is always
twice the radius, we can replace two 𝑟 with 𝑑 to give an equation in terms of
𝑑. Alternatively, we could solve our
previous equation for 𝑟 and double its value at the end.
To solve our equation for 𝑑, we
can first cancel a factor of 𝜋 from both sides to give 434 is equal to 31𝑑. Finally, we divide both sides of
the equation by 31. And we have that 𝑑 is equal to
14. Including the length units, we’ve
found that the diameter of the base of the given cylinder is 14 centimeters.
