Tennis balls have a surface area of 43.56π cm2 . Which of the following cylinders could fit 3 tennis balls?
To find the volume of a tennis ball, we first need to find the radius of the tennis ball.
The formula for the surface area of a sphere is 4πr^2, where r is the radius of the sphere.
Given that the surface area of the tennis ball is 43.56π cm^2, we can set up the following equation:
4πr^2 = 43.56π
Dividing by 4π on both sides, we get:
r^2 = 10.89
Taking the square root of both sides, we find that r = √10.89 = 3.3 cm.
Now, we can calculate the volume of a tennis ball using the formula V = (4/3)πr^3:
V = (4/3)π(3.3)^3
V ≈ 153.77 cm^3
Since we want to fit 3 tennis balls into a cylinder, we need to find a cylinder with a volume of at least 3 times the volume of a tennis ball. Therefore, the minimum volume required for the cylinder is:
3 * 153.77 cm^3 = 461.31 cm^3
The formula for the volume of a cylinder is V = πr^2h, where r is the radius of the base of the cylinder and h is the height of the cylinder.
Given that we need the volume of the cylinder to be at least 461.31 cm^3, we can try to calculate the radius and height for a cylinder that can accommodate 3 tennis balls.
Let's take the radius of the base of the cylinder to be equal to the radius of the tennis ball, which is 3.3 cm. We can calculate the height of the cylinder using the formula:
461.31 = π(3.3)^2h
461.31 = 34.23h
h = 13.47 cm
Therefore, a cylinder with a radius of 3.3 cm and a height of 13.47 cm could fit 3 tennis balls.