Surface Area & Volume of Spheres Section 11-6
Feb 23, 2016
Surface Area & Volume of Spheres
Section 11-6
Vocab• Sphere - the set of all points in space
equidistant from a given point called the center.
• Radius - segment that has one endpoint at the center and the other endpoint on the sphere.
• Diameter - segment passing through the center with endpoints on the sphere.
Surface Area of a Sphere
= 324 Simplify.
Find the surface area of the sphere below. Leave your answer in terms of .
S.A. = 4 r 2 Use the formula for the surface area of a sphere.
= 4 • 92 Substitute r = = 9.18 2
The surface area of the sphere is 324 ft2.
Your turn• Find the S.A. of a sphere with a
diameter of 14 in. Give your answer two ways, in terms of π and rounded to the nearest square inch.
• 196π in2; 616 in2
S.A. = 4 r 2 Use the formula for the surface area of a sphere.
13 = 2 r Substitute 13 for C. C = 2 r Use the formula for circumference.Step 1: Use the circumference to find the radius in terms of .
The circumference of a rubber ball is 13 cm. Calculate its surface area to the nearest whole number.
= r Solve for r.132Step 2: Use the radius to find the surface area.
= 4 • ( )2 Substitute for r.132
132
To the nearest whole number, the surface area of the rubber ball is 54 cm2.
= Simplify.169
53.794371 Use a calculator.
Your turn• Find the S.A. of a melon with a
circumference of 18 in. Round your answer to the nearest ten square inches.
• 100 in2
Volume of a sphere
Find the volume of the sphere. Leave your answer in terms of .
V = r 3 Use the formula for the volume of a sphere.43
302 = • 153 Substitute r = = 15.4
3
= 4500 Simplify.
The volume of the sphere is 4500 cm3.
Your turn• Find the volume to the nearest
cubic inch of a sphere with a diameter of 60 inches.
• 113,097 in3
The volume of a sphere is 1 in.3. Find its surface area to the nearest tenth.
Step 1: Use the volume to find the radius r.
V = r 3 Use the formula for the volume of a sphere.43
1 = r 3 Substitute.43
= r 3 Solve for r 3. 34
= r Find the cube root of each side. 34
3
r 0.62035049 Use a calculator.
Step 2: Use the radius to find the surface area.
S.A. = 4 r 2 Use the formula for the surface area of a sphere.
4 (0.62035049)2 Substitute.
4.8359744 Use a calculator.
To the nearest tenth, the surface area of the sphere is 4.8 in.2.
(continued)
Your Turn• The volume of a sphere is 4200 ft3.
Find S.A. to the nearest tenth.• 1258.9 ft3