Doug has a bucket that is 12in tall and has a radius of 6in filled completely with water. Dough pushes a basketball with a diameter of 10in completely into the water overflowing the water in the bucket. How much water is left in the bucket?

Answer 1

First, let's find the volume of water that was in the bucket before the basketball was pushed in.

The volume of a cylinder (the shape of the bucket) is given by the formula V = πr^2h, where r is the radius and h is the height.

Given that the radius is 6 inches and the height is 12 inches, the initial volume of water in the bucket is:
V_initial = π(6)^2(12) = 432π cubic inches

Next, let's find the volume of the basketball. The volume of a sphere (the shape of a basketball) is given by the formula V = 4/3 πr^3, where r is the radius.

Given that the diameter of the basketball is 10 inches (radius = 5 inches), the volume of the basketball is:
V_ball = 4/3 π(5)^3 = 523.6 cubic inches

Since the basketball was pushed completely into the water, it displaced an equal volume of water. Therefore, the final volume of water in the bucket is:
V_final = V_initial - V_ball
V_final = 432π - 523.6
V_final ≈ 108.8 cubic inches

Therefore, there is approximately 108.8 cubic inches of water left in the bucket after the basketball is pushed in.