We want to find the volume of a tennis ball knowing that its circumference is 8 inches. We will begin by finding its radius using that the circumference of a sphere is two times the product of π and the radius.
C=2π rBy substituting 8 for C we can find r.
8=2π r ⇔ r=8/2π= 4/π
The volume of a sphere is four thirds the product of π and the cube of the radius.
V=4/3π r^3
Let's substitute 4π for r in the above formula and simplify the right-hand side.
The volume of a tennis ball is about 8.6 inches^3.
b
To find how much of the cylinder is not taken up by the three tennis balls stored in it we will first find the volume of the cylinder. Then we will calculate the volume of the three tennis balls and subtract them from the can's volume. Let's do it!
Volume of the Cylinder
We have a cylinder with a radius of 1.43 inches and height of 8 inches, and we want to find its volume. The volume of a cylinder is the product of the area of the base and the height.
V= BhOur cylinder has a circular base, B, and its area is the product of π and the radius squared.
V= Bh ⇒ V = π r^2 h
Let's substitute the corresponding values into the formula and find its volume.
In Part A we found that the volume of one tennis ball is 2563 π^2 inches^3. The volume of three tennis balls is three times this volume.
V_(tennis balls)=3 * 256/3 π^2= 256/π^2 in^3
Volume Not Taken Up By Tennis Balls
To find the volume not taken up by the tennis balls, V_(not tennis balls), we will subtract the volume of the cylinder by the volume of the tennis balls.
V_(not tennis balls)= V_(cylinder)- V_(tennis balls)
⇓
V_(not tennis balls)= 16.3592π- 256/π^2 ≈ 25.4
To find the volume not taken up by the tennis balls is approximately 25.4 inches^2
