13.3 Volumes of spheres. By Kylie Bolton and Jessica Nguyen. Objectives. Find volumes of spheres and hemispheres. Solve problems involving volumes of spheres and hemispheres with given diameters, radius’, surface areas, and circumferences. What is a Sphere?.
By Kylie Bolton and Jessica Nguyen
Finding the volume of a sphere is kind of like finding the volume of a pyramid and the surface area of a sphere.
Suppose that the space inside a sphere is divided into an infinite number of near pyramids with all their vertices on the center of the sphere. The height of the pyramid equals the radius of the sphere.
The sum of all the pyramids’ bases will equal the surface area of the entire sphere. The sum of all the pyramids’ volume is equal to the volume of the sphere.
Also, the surface area of a sphere, 4∏r², is equal to B1 + B2 + B3 +…+ Bn
Sum of the volumes of all the pyramids.
Replace h with r.
V=1/3B¹h¹ + 1/3B²h² + 1/3B³h³ +…+ 1/3Bnhn
=1/3B1r + 1/3B2r + 1/3B3r +…+ 1/3Bnr
=1/3r(B1 +B2 + B3 +…+ Bn)
Plug it in!
Find the volume of this hemisphere with a radius of 2in.
1. Plug the radius into the formula V=1/2(4/3r³)
Find the volume of the hemisphere if the surface area=10
Round to the nearest 10th
Pg. 704 #3-7, 9-20, 23-24, 30-31
By Jessica and Kylie!