Geometry Notes G.13 Spheres, Similar Solids
Mrs. Grieser
Name: _________________________________________ Date: _______________ Block: _______
Spheres

Sphere: Set of all points in space equidistant from a given
point.

Center: The given point is the center of the sphere.

Radius: Segment from the center of a sphere to a point on
the sphere.

Chord: Segment whose endpoints are on a sphere.

Diameter: Chord that contains the center of a sphere.
Surface Area and Volume of a Sphere
Spheres
Surface Area: SA  4 r 2
4
Volume: V   r 3
3
Examples:
a) Find the surface area
of the sphere:
b) The surface area of a sphere
is 12.25π cm2. Find the
sphere’s diameter.
c) The bowling ball has a
diameter of 8 inches. Find
its volume.
d) Find the radius of a sphere when
V = 1436.76 m3.
You try:
a) The diameter of a sphere is 50 ft. Find the
surface area.
b) The surface area of a sphere is 36π m2. Find
the radius.
c) The radius of a sphere is 7 yds. Find the
volume of the sphere.
d) Find the radius of a sphere when
V = 91.95 m3.
Geometry Notes G.13 Spheres, Similar Solids
Mrs. Grieser Page 2
Similar Solids

Solids are similar if they have equal ratios of corresponding linear measures, such as
height or radii

We know that for polygons, the ratio of areas is a2:b2, where a:b is the ratio of side
lengths
For solids:
If two similar solids have a scale factor of a:b, then


the ratio of areas is a2:b2
the ratio of volumes is a3:b3
Examples:
a) The cans shown are similar with a scale
factor of 67:100. The surface area and
volume of the smaller can are SA1 = 40.73
in2 and V1 = 17.16 in3. Find the surface
area and volume of the larger can.
b) The pyramids are similar. Pyramid P has a
volume of 125 in3 and Pyramid Q has a
volume of 64 in3. Find the scale factor of
Pyramid P to Pyramid Q.
You try:
a) Cylinder A is similar to cylinder B (not
shown) with scale factor A:B of 1:2. Find the
surface area and volume of B.
b) Cone A is similar to cone B (not shown) with
scale factor A:B of 5:2. Find the surface area
and volume of B.
c) The solids are similar. Find the scale factor
of I:II.
d) The solids are similar. Find the scale factor
of I:II.