Tennis balls have a surface area of 43.56 cm^2 which of the following cylinders could fit 3 tennis balls?? A. cylinder with a radius of 3.3 and a height of 20? B. A cylinder with a radius of 3.3 and a height of 10. C. A cylinder with a radius of 1.9 and height of 6 cm D. A cylinder with a radius of 1.9 can and a height of 12 cm
To determine which cylinder could fit 3 tennis balls, we first need to calculate the volume of one tennis ball. The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere.
The diameter of a tennis ball is approximately 6.7 cm, so the radius of a tennis ball is half of that, which is 3.35 cm.
Therefore, the volume of one tennis ball is V = (4/3)π(3.35)^3 ≈ 164.52 cm^3
Since we want to fit 3 tennis balls, the total volume needed is 3 * 164.52 = 493.56 cm^3
Next, we calculate the volume of each cylinder. The formula for the volume of a cylinder is V = πr^2h, where r is the radius of the base and h is the height.
A. Cylinder with a radius of 3.3 cm and a height of 20 cm:
V = π(3.3)^2(20) ≈ 686.65 cm^3
B. Cylinder with a radius of 3.3 cm and a height of 10 cm:
V = π(3.3)^2(10) ≈ 343.32 cm^3
C. Cylinder with a radius of 1.9 cm and a height of 6 cm:
V = π(1.9)^2(6) ≈ 64.54 cm^3
D. Cylinder with a radius of 1.9 cm and a height of 12 cm:
V = π(1.9)^2(12) ≈ 145.01 cm^3
Therefore, the cylinder that could fit 3 tennis balls is option B, as it has a volume of 343.32 cm^3, which is greater than the required volume of 493.56 cm^3.