Surface Area & Volume of Spheres
If you cut a sphere right down the middle you would create two congruent halves called HEMISPHERES.
You can think of Earth.
The equator cuts Earth into the northern and southern hemisphere.
Look at the cross section formed when you cut a sphere in half.
What shape is it?
A circle!!! This is called the GREAT CIRCLE of the sphere.
r
Radius of a Sphere
Surface Area of a Sphere
8 in
Surface Area of a Sphere
(round to the nearest hundredths)
10 cm
Surface Area of a Sphere
(round to the nearest hundredths)
Volume of a Sphere
2 cm
Volume of a Sphere
(round to the nearest hundredths)
10 cm
Volume of a Sphere
(round to the nearest hundredths)
25 in
The circumference of a great circle of a sphere is 25 inches. Find the volume of the sphere. (Round to the nearest hundredths.)
Ratio Relationships
a:b Ratio of the scale factor
a:b Ratio of the corresponding sides
a:b Ratio of the perimeters
a2:b2 Ratio of the area
a3:b3 Ratio of the volume
5 in
Volume of a Sphere
A spherical balloon has an initial radius of 5 in. When more air is added, the radius becomes 10 in. Explain how the volume changes as the radius changes.
10 in
5:10 or 1:2. So 13:23 means the volume would be 8 times as much.
Volume of a Sphere
A sphere has an initial volume of 400 cm.3 The sphere is made bigger by making the radius 4 times as big. What is the new volume of the sphere?
1:4
So, 13:43 means the volume would be 64 times more volume.
64 times 400 =
16 cm.
Volume of a Sphere
A sphere is inscribed in a cube-shaped box as pictured below. To the nearest centimeter, what is the volume of the empty space in the box?
10 in