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?
First, let's find the volume of the water in the bucket before the basketball is pushed in.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
Given:
Radius (r) = 6in
Height (h) = 12in
V = π(6^2)(12)
V = π(36)(12)
V = π(432)
V ≈ 1357.17 cubic inches
Now let's find the volume of the basketball. The volume of a sphere is given by the formula V = 4/3 πr^3, where r is the radius.
Given:
Radius (r) = 5in (half the diameter of the basketball)
V = 4/3 π(5^3)
V ≈ 523.6 cubic inches
When the basketball is pushed into the water, some of the water will overflow. The amount of water it displaces is equal to the volume of the basketball.
Therefore, the amount of water left in the bucket will be the initial volume of water in the bucket minus the volume of the basketball:
Water left = 1357.17 - 523.6
Water left ≈ 833.57 cubic inches
So, there will be approximately 833.57 cubic inches of water left in the bucket.