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?
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.