Algebra & Analytic Geometry
3D Solids – Spheres
Name & Date
A sphere is the locus of points in space that are a fixed distance
from a given point called the center of a sphere.
A radius of the sphere connects the center of the sphere to any
point on the sphere.
A hemisphere is half of a sphere.
A great circle divides a sphere into two hemispheres
**Surface Area
**Volume
SA  4 r 2
V 
4 3
r
3
1) Find the exact surface area and volume of the sphere pictured below.
Surface Area
Volume
2) Find the exact surface area and volume of the sphere pictured below.
Surface Area
Volume
3) The surface area of a sphere is approximately 118in 2 .
A) Find the radius to the nearest tenth of an inch.
B) Find its volume.
4) The surface area of a sphere is 700  cm 2 .
A) Find the radius of the sphere.
B) Find its volume.
5) The circumference of a great circle of a sphere is 28  cm.
A) Find its surface area.
B) Find its volume.
6) The volume of a sphere is 972  ft 3 .
A) Find its radius.
B) Find its surface area.
Algebra & Analytic Geometry
3D Solids – Spheres
Name & Date
7) A sphere has the same volume as a square prism with height 10 in. and base with a 28-inch perimeter. What
is the radius of the sphere? Round to the nearest tenth.
8) The great circle of a sphere has a circumference of 30π. Calculate its volume and surface area. Leave both
answers exact.
9) Find the volume of a hemisphere with radius 9. Leave answer in exact form.
10) Find the volume AND surface area of the figure to the right. The great circle of the hemisphere is the
base of the cylinder.
11) Calculate the volume and surface area of a sphere with a great circle of area 36π in2.
12) The volume of a sphere is 972π in3. Calculate the surface area.
13) The surface area of a sphere is 1936π in2. Calculate the volume.
14) Calculate the surface area of a hemisphere with volume 3888πcm2.
15) A solid is composed of a cone and a hemisphere that share the same base with circumference 12πinches.
First draw the figure, then calculate the volume of the figure if the cone has a height of 10 inches.
Algebra & Analytic Geometry
3D Solids – Spheres
Name & Date
16) Find the volume of the figure to the right if the circumference of the great circle of the hemisphere is
16π inches and the height of the cones is 10 inches.
17) The surface area of a cone is 485.4 ft2. If the radius of the base is 8 ft, find the volume of the cone.
18) The volume of a hemisphere is 144π cm3. Calculate its surface area.
19) The volume of a sphere is 18432π in3. Find its exact surface area.