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

To find the volume of water that overflowed when the basketball was pushed into the bucket, we need to calculate the volume of the basketball and subtract it from the volume of the bucket.

The volume of a sphere can be calculated using the formula V = (4/3)πr^3, where r is the radius of the sphere.

For the basketball:
r = 5 inches (half of the diameter)
V = (4/3) * π * 5^3 = (4/3) * π * 125 = 523.6 cubic inches

Now, let's calculate the volume of the bucket:
V = π * r^2 * h, where r = 6 inches (radius) and h = 12 inches (height)
V = π * 6^2 * 12 = π * 36 * 12 = 1360.8 cubic inches

Since the basketball volume is smaller than the bucket volume, the water will overflow the bucket.

The amount of water left in the bucket can be calculated by subtracting the volume of the basketball from the volume of the bucket:
1360.8 cu in - 523.6 cu in = 837.2 cubic inches

Therefore, there are 837.2 cubic inches of water left in the bucket after the basketball is pushed in.