Page 57 - Math Course 3 (Book 2)

Geometric Surface Area: Spheres

Surface Area
Next, find the surface area of the sphere. Be sure to
round to the nearest tenth.
Example
T = 4 r² Surface area of a sphere.

Find the surface area of the sphere, given a great
circle with an area of approximately 907.9 square = 4 (3.8)² r ≈ 3.8
centimeters
≈ 183.3 Use a calculator.
The surface area of a sphere is four times the
area of the great circle.
The surface area is approximately
Answer
T = 4 r² Surface area of a sphere. 183.3 square inches.

= 4(907.9) r² = 907.9
Your Turn!
≈ 3631.6 Multiply.
Spheres and Circles
In the figure, O is the center of the sphere, and
The surface area is approximately plane U intersects the sphere in circle L. If OL = 3
Answer
3631.6 square centimeters. inches and LM = 8 inches, find OM to the nearest
tenth.
Find the surface area of a hemisphere with a
radius of 3.8 inches. A. 7.4 in.
B. 8.5 in.
A hemisphere is half of a sphere. To find the C. 11 in.
surface area, find half of the surface area of the D. 8.7 in.
sphere and add the area of the great circle.

1 Surface area of
surface area = (4 r²) + r²
2 a hemisphere
1
= [4 (3.8)²] + (3.8)² Substitution.
2
Use a
≈ 136.1
calculator.

The surface area is approximately
Answer Answer
136.1 square inches.

Standardized Test Example Surface Area
Find the approximate surface area of the sphere,
Find the surface area of a ball with a circumfer- given a great circle with an area of approximately
ence of 24 inches to determine approximately how 91.6 square centimeters.
much leather is needed to make the ball.
A. 183.2 cm²
First, find the radius of the sphere. B. 366.4 cm²
C. 287.8 cm²
C = 2 r Circumference of a circle D. 1151.1 cm²

24 = 2 r C = 24
Answer
24
= r Divide each side by 2
2
3.8 ≈ r Use a calculator.

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