A bowling ball is a solid ball with a spherical surface and diameter 30 cm. To custom fit a bowling ball for each bowler, three holes are drilled in the ball. Bowler Kris has holes drilled that are 8 cm deep and have diameters of 2 cm, 2 cm, and 3 cm. Assuming the three holes are right circular cylinders, find the number of cubic centimeters in the volume of the fitted bowling ball. Express your answer in terms of pi.
I have no idea how to do this problem, could you guys please help?
The answer is 4466 Pi because the volume of the ball itself is 4500 pi and the volume of the three holes are 34pi. Thus, 4500pi-34pi=4466pi.
sure you have an idea.
You know how to finds the volume of a sphere, right?
You know how to find the volume of a cylinder, right?
So, find the volume of each cylinder, add them up and subtract that from the volums of the sphere.
Done. What's you get?
Why did the bowling ball go to the doctor?
Because it couldn't find any "spare" holes! 😄
Now, let's dive into the problem. We need to calculate the volume of the fitted bowling ball after the holes are drilled.
To find the volume of the fitted ball, let's start by calculating the volume of the original bowling ball. The formula for the volume of a sphere is:
V_ball = (4/3) * π * r^3
Given that the diameter of the bowling ball is 30 cm, we can find the radius (r) by dividing the diameter by 2:
r = 30 cm / 2 = 15 cm
Substituting the radius value into the formula, we get:
V_ball = (4/3) * π * (15 cm)^3
Moving on to the drilled holes, we have three cylinders with the following dimensions:
Hole 1:
- Depth (h1) = 8 cm
- Radius (r1) = 1 cm (half the diameter of 2 cm)
Hole 2:
- Depth (h2) = 8 cm
- Radius (r2) = 1 cm (half the diameter of 2 cm)
Hole 3:
- Depth (h3) = 8 cm
- Radius (r3) = 1.5 cm (half the diameter of 3 cm)
The formula for the volume of a cylinder is:
V_cylinder = π * r^2 * h
Therefore, the volume of each hole is:
V_hole1 = π * (1 cm)^2 * 8 cm
V_hole2 = π * (1 cm)^2 * 8 cm
V_hole3 = π * (1.5 cm)^2 * 8 cm
To find the volume of the fitted bowling ball, we subtract the sum of the volumes of the holes from the volume of the original ball:
V_fittedball = V_ball - (V_hole1 + V_hole2 + V_hole3)
Now you just need to plug in the values and do the calculations to find the final answer.
Sure! To find the volume of the fitted bowling ball, we need to subtract the volume of the three holes drilled from the volume of the original bowling ball.
First, let's find the volume of the original bowling ball. The formula for the volume of a sphere is given by V = (4/3) * pi * r^3, where r is the radius. In this case, the diameter of the ball is 30 cm, so the radius is half of that, which is 15 cm.
Substituting the values into the formula, we have:
V_ball = (4/3) * pi * (15 cm)^3
Now, let's find the volume of the three holes. The formula for the volume of a cylinder is given by V = pi * r^2 * h, where r is the radius and h is the height. We have three cylinders with different diameters and depths, so we need to calculate the volumes of each cylinder separately and then add them up.
For the first hole:
radius = 1 cm (half of the diameter, which is 2 cm)
depth = 8 cm
V_hole1 = pi * (1 cm)^2 * 8 cm
For the second hole:
radius = 1 cm (same diameter as the previous hole)
depth = 8 cm
V_hole2 = pi * (1 cm)^2 * 8 cm
For the third hole:
radius = 1.5 cm (half of the diameter, which is 3 cm)
depth = 8 cm
V_hole3 = pi * (1.5 cm)^2 * 8 cm
Now, let's calculate the total volume of the holes by adding the volumes of the three cylinders:
V_holes = V_hole1 + V_hole2 + V_hole3
Finally, we can calculate the volume of the fitted bowling ball by subtracting the total volume of the holes from the volume of the original ball:
V_fitted_ball = V_ball - V_holes
So, the number of cubic centimeters in the volume of the fitted bowling ball is given by V_fitted_ball, expressed in terms of pi.