Parts of a ball and the oblique prism
Find the area of a spherical zone, the volume of a segment and of a sector of a ball, and the volume of an oblique prism. Type answers with π: 20π is entered as 20π.
- Russia: grade 11
Guide
Zone of a sphere: S = 2πRh with h the height of the zone. Segment of a ball: V = πh²(R − h/3). Sector of a ball: V = 2/3 πR²h with h the height of its cap. Oblique prism: V = base area × height H, where H is the distance between the bases, not the length of the slanted edge.
Why does an oblique prism have the same volume as a right prism with the same base and height? Cavalieri's principle: if every slice at the same level has the same area, the volumes are equal.
Type the answer with the π button under the box.