Question

A cylindrical canister contains three tennis balls. Assume the tennis balls touch the sides of the canister and the top and bottom with no gaps. If each ball is 2.7 inches in diameter, how much wasted space is in the canister? Round to the nearest hundredth. A) 10.31 in3 B) 15.46 in3 C) 18.04 in3 D) 30.92 in

Answer 1

The answer is (B) for this question

Answer 2

Answer:

Option B) 15.46 inch³

Step-by-step explanation:

A cylindrical container contains three tennis balls.These balls touch the sides of the container and the top and the bottom with no gaps.

Therefore radius and height of the cylindrical container will be decided by the radius of single tennis ball and total of diameters of the balls respectively.

To be more clear radius of the container = radius of the ball = 2.7/2 = 1.35 inches

Height of the container = 3× diameter of a ball = 3×2.7 = 8.1 inches

Now wasted space in the container = volume of container - 3×volume of a ball

volume of the cylindrical container = π×r²×h = 3.14 × (1.35)²×(8.1) = 46.36 inch³

Volume of a ball = (4/3)×π×r³ = (4/3)×3.14×(1.35)³ = 10.30 inch³

Wasted space = 46.36 - 3×(10.30) = 46.36 - 30.90 = 15.46 inch³

Option B is the answer.