Tennis balls have a surface area of 43.56π cm2. Which of the following cylinders could fit 3 tennis balls?(1 point)

Question

Responses

a cylinder with a radius of 3.3 cm and a height of 10 cm

a cylinder with a radius of 1.9 cm and a height of 6 cm

a cylinder with a radius of 3.3 cm and a height of 20 cm

a cylinder with a radius of 1.9 cm and a height of 12 cm

Answer 1

To determine which cylinder could fit 3 tennis balls, we first need to calculate the volume of a tennis ball using the given surface area.

The surface area of the tennis ball formula is given by 4πr^2, where r is the radius of the tennis ball.

Given a surface area of 43.56π cm^2, we can solve for the radius of the tennis ball:

43.56π = 4πr^2
r^2 = 43.56/4
r = √(10.89) = 3.3 cm

Now, we have the radius of the tennis ball, and we can calculate its volume:

Volume = (4/3)πr^3
Volume = (4/3)π(3.3)^3
Volume = (4/3)π(35.937)
Volume = 151.364π cm^3

Next, we need to calculate the volume of each cylinder to see if 3 tennis balls can fit inside.

a) Cylinder with a radius of 3.3 cm and a height of 10 cm:
Volume = π(3.3)^2(10) = 108.9π cm^3

b) Cylinder with a radius of 1.9 cm and a height of 6 cm:
Volume = π(1.9)^2(6) = 64.692π cm^3

c) Cylinder with a radius of 3.3 cm and a height of 20 cm:
Volume = π(3.3)^2(20) = 217.8π cm^3

d) Cylinder with a radius of 1.9 cm and a height of 12 cm:
Volume = π(1.9)^2(12) = 87.432π cm^3

From the volume calculations, it is clear that only the cylinder with a radius of 3.3 cm and a height of 20 cm (c) has enough volume to fit 3 tennis balls.