Question

A cap of a sphere is generated by rotating the shaded region in about the y-axis.

1. volume = 14/3 π cu. ins
2. volume = 6 π cu. ins
3. volume = 16/3 π cu. ins
4. volume = 17/3 π cu. ins
5. volume = 5 π cu. ins
Determine the volume of this cap when the radius of the sphere is 6 inches and the height of the cap is 2 inchs.

Answer 1

The volume of the spherical cap, with a sphere radius of 6 inches and cap height of 2 inches, calculated using the formula for a spherical cap's volume is 21.333\u03c0 cubic inches, which does not match any of the provided options.

Step-by-step explanation:

The volume of a spherical cap can be calculated using the formula V = (1/3)\u03c0h²(3R - h), where R is the radius of the sphere and h is the height of the cap. In this case, since the radius R is 6 inches and the height h of the cap is 2 inches, the formula becomes V = (1/3)\u03c0(2²)(3\u00d76 - 2). Substitute the values to get V = (1/3)\u03c0(4)(18 - 2) = (1/3)\u03c0(4)(16), which calculates to V = (64/3)\u03c0 cubic inches, which simplifies to V = 21.333\u03c0 cubic inches. This result is not listed in the provided options, which suggests a possible error in the question or answer choices.