Tennis balls have a surface area of 43.56π cm2 . Which of the following cylinders could fit 3 tennis balls?(1 point)
Responses
a cylinder with a radius of 3.3 cm and a height of 10 cm
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 12 cm
a cylinder with a radius of 1.9 cm and a height of 12 cm
a cylinder with a radius of 1.9 cm and a height of 6 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
Based on the surface area of the tennis balls (43.56π cm^2) and the formula for the lateral surface area of a cylinder (2πrh), we can calculate the minimum lateral surface area needed to fit 3 tennis balls.
For the first option:
Lateral surface area = 2π(3.3)(10) = 66π cm^2
For the second option:
Lateral surface area = 2π(1.9)(12) = 45.36π cm^2
For the third option:
Lateral surface area = 2π(1.9)(6) = 22.68π cm^2
For the fourth option:
Lateral surface area = 2π(3.3)(20) = 132π cm^2
Based on these calculations, the second option, a cylinder with a radius of 1.9 cm and a height of 12 cm, has a lateral surface area closest to 3 times the surface area of the tennis balls, so it is the cylinder that could fit 3 tennis balls.