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Chapter 12.6. Surface Area and Volume of Spheres. Concept. Surface Area of a Sphere. Example 1. Find the surface area of the sphere. Round to the nearest tenth. S = 4 r 2 Surface area of a sphere = 4 (4.5) 2 Replace r with 4.5. ≈ 254.5 Simplify. Answer: 254.5 in 2.
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Chapter 12.6 Surface Area and Volume of Spheres
Surface Area of a Sphere Example 1 Find the surface area of the sphere. Round to the nearest tenth. S = 4r2 Surface area of a sphere = 4(4.5)2 Replace r with 4.5. ≈ 254.5 Simplify. Answer: 254.5 in2
Example 1 Find the surface area of the sphere. Round to the nearest tenth. A. 462.7 in2 B. 473.1 in2 C. 482.6 in2 D. 490.9 in2
Use Great Circles to Find Surface Area Example 2A A. Find the surface area of the hemisphere. Find half the area of a sphere with the radius of 3.7 millimeters. Then add the area of the great circle.
Use Great Circles to Find Surface Area Example 2B B. Find the surface area of a sphere if the circumference of the great circle is 10 feet. First, find the radius. The circumference of a great circle is 2r. So, 2r = 10 or r = 5.
Use Great Circles to Find Surface Area Example 2C C. Find the surface area of a sphere if the area of the great circle is approximately 220 square meters. First, find the radius. The area of a great circle is r2. So, r2 = 220 or r≈ 8.4.
Example 2A A. Find the surface area of the hemisphere. A. 110.8 m2 B. 166.3 m2 C. 169.5 m2 D. 172.8 m2
Example 2B B. Find the surface area of a sphere if the circumference of the great circle is 8 feet. A. 100.5 ft2 B. 201.1 ft2 C. 402.2 ft2 D. 804.3 ft2
Example 2C C. Find the surface area of the sphere if the area of the great circle is approximately 160 square meters. A. 320 ft2 B. 440 ft2 C. 640 ft2 D. 720 ft2
(15)3r = 15 Volumes of Spheres and Hemispheres Example 3A A. Find the volume a sphere with a great circle circumference of 30 centimeters. Round to the nearest tenth. Find the radius of the sphere. The circumference of a great circle is 2r. So, 2r = 30 or r = 15. ≈ 14,137.2 cm3
r 3 Use a calculator. Volumes of Spheres and Hemispheres Example 3B B. Find the volume of the hemisphere with a diameter of 6 feet. Round to the nearest tenth. The volume of a hemisphere is one-half the volume of the sphere. Volume of a hemisphere Answer: The volume of the hemisphere is approximately 56.5 cubic feet.
Example 3A A. Find the volume of the sphere to the nearest tenth. A. 268.1 cm3 B. 1608.5 cm3 C. 2144.7 cm3 D. 6434 cm3
Example 3B B. Find the volume of the hemisphere to the nearest tenth. A. 3351.0 m3 B. 6702.1 m3 C. 268,082.6 m3 D. 134,041.3 m3
Solve Problems Involving Solids Example 4 ARCHEOLOGYThe stone spheres of Costa Rica were made by forming granodiorite boulders into spheres. One of the stone spheres has a volume of about 36,000 cubic inches. What is the diameter of the stone sphere? Understand You know that the volume of the stone is 36,000 cubic inches. Plan First use the volume formula to find the radius. Then find the diameter.
Example 4 RECESS The jungle gym outside of Jada’s school is a perfect hemisphere. It has a volume of 4,000 cubic feet. What is the diameter of the jungle gym? A. 10.7 feet B. 12.6 feet C. 14.4 feet D. 36.3 feet