Find the volume of a cap of a sphere with radius r=86 and height h=48.
To find the volume of a cap of a sphere, you'll first need to calculate the volume of the sphere and then subtract the volume of the spherical segment.
Here's how you can go about it:
Step 1: Calculate the volume of the sphere.
The volume of a sphere is given by the formula:
V_sphere = (4/3) * π * r^3
where r is the radius of the sphere.
In this case, the radius of the sphere is 86, so we can substitute that value into the formula:
V_sphere = (4/3) * π * 86^3
Step 2: Calculate the volume of the spherical segment.
The volume of a spherical segment is given by the formula:
V_segment = (1/6) * π * h^2 * (3r - h)
where r is the radius of the sphere and h is the height of the segment.
In this case, the radius of the sphere is 86 and the height of the segment is 48, so we can substitute those values into the formula:
V_segment = (1/6) * π * 48^2 * (3*86 - 48)
Step 3: Calculate the volume of the cap.
The volume of the cap is given by subtracting the volume of the segment from the volume of the sphere:
V_cap = V_sphere - V_segment
Now, you can substitute the respective values into the formula and calculate the volume of the cap.