12. 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, we need to calculate the volume of water in the bucket before the basketball was pushed in.

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

So, the volume of water in the bucket before pushing the basketball in is:
V = π(6in)^2(12in)
V = π(36in^2)(12in)
V = π(432in^3)
V ≈ 1357.17 in^3

Next, we calculate the volume of the basketball pushed into the bucket. We have to find the radius of the basketball, which is half of the diameter:
r = 10in / 2
r = 5in

The volume of a sphere (basketball) is given by the formula V = (4/3)πr^3. So, the volume of the basketball is:
V = (4/3)π(5in)^3
V = (4/3)π(125in^3)
V ≈ 523.60 in^3

Now, we subtract the volume of the basketball from the original volume of water in the bucket to find out how much water is left:
Water left = 1357.17 in^3 - 523.60 in^3
Water left ≈ 833.57 in^3

Therefore, there is approximately 833.57 in^3 of water left in the bucket.