12.6 surface area and volume of spheres ink.notebook · 12.6 surface area and volume of spheres...
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12.6 surface area and volume of spheres ink.notebook
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May 02, 2018
Page 171
12.6 Surface Area and Volume of Spheres
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Page 173 Page 174Page 175
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Lesson Objectives Standards Lesson Notes
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12.6 Surface Area and Volume of Spheres
Lesson Objectives
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Lesson NotesStandards
After this lesson, you should be able to successfully find the surface area and volume of spheres.
Lesson Objectives Standards Lesson NotesG.MG.1 Use geometric shapes, their measures, and their properties to describe objects.G.GMD.4 Identify the shapes of twodimensional cross sections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects.G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.G.MG.2 Apply concepts of density based on area and volume in modeling situations.
A sphere is the locus of points in space
that are a fixed distance from a given
point called the _______. A
________ connects the center of the
sphere to any point on the sphere. A
___________ is half of a sphere. A
_______________ divides a sphere
into two hemispheres.
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Surface Areas of Spheres You can think of the surface area of a sphere as the total area of all of the nonoverlapping strips it would take to cover the sphere. If r is the radius of the sphere, then the area of a great circle of the sphere is πr2. The total surface area of the sphere is four times the area of a great circle.
Surface Area of a SphereIf a sphere has a surface area of SA square units and a radius of r units, then
SA = 4πr2. Surface Area = 4π(radius)2
1. Find the surface area of a sphere to the nearest tenth if the radius of the sphere is 6 cm.
SA = 4πr2
Find the surface area of the sphere. Round to the nearest tenth.
2. 3. Find the surface area of the sphere. Round to the nearest tenth.
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Volumes of Spheres A sphere has one basic measurement, the length of its radius. If you know the length of the radius of a sphere, you can calculate its volume.
Volume of a Sphere If a sphere has a volume of V cubic units and a radius of r units, then
Volume of a sphere =
Find the volume of each sphere or hemisphere. Round to the nearest tenth.
6.4. 5.
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7. hemisphere: radius 5 in.
8. sphere: circumference of great circle ≈ 25 ft
Find the volume of each sphere or hemisphere. Round to the nearest tenth.
9. hemisphere: area of great circle ≈ 50 m2
Find the volume of each sphere or hemisphere. Round to the nearest tenth.
10. ORANGES Mandy cuts a spherical orange in half along a great circle. If the radius of the orange is 2 inches, what is the area of the cross section that Mandy cut? Round your answer to the nearest hundredth. What is the volume of her HALF an orange?
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The density of a metal is a ratio of its mass to its volume. For example, the mass of aluminum is 2.7 grams per cubic centimeter. Here is a list of several metals and their densities.
To calculate the mass of a piece of metal, multiply volume by density.Example Find the mass of a silver ball that is 0.8 cm in diameter.M = D · V
The mass is about 2.81 grams.=
11. Find the mass of a copper ball 0.8 cm in diameter
To calculate the mass of a piece of metal, multiply volume by density.
12. Find the mass of a gold ball 2 cm in diameter
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On the Worksheet
HOMEWORK
12.6 Practice WS Surface Areas and Volumes of Spheres
Find the surface area of each sphere. Round to the nearest tenth.
1. 2.Find the surface area of each sphere. Round to the nearest tenth.
3.
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Find the volume of each sphere or hemisphere. Round to the nearest tenth.4. 5.
Find the volume of each sphere or hemisphere. Round to the nearest tenth.6.
Find the volume of each sphere or hemisphere. Round to the nearest tenth.7. hemisphere: diameter = 48 yd
Find the volume of each sphere or hemisphere. Round to the nearest tenth.
8. sphere: circumference ≈ 26 m
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9. MOONS OF SATURN The planet Saturn has several moons. These can be modeled accurately by spheres. Saturn's largest moon Titan has a radius of about 2575 kilometers. What is the approximate surface area of Titan? Round your answer to the nearest tenth.
10. BILLIARDS A billiard ball set consists of 16 spheres, each inches in diameter. What is the total volume of
a complete set of billiard balls? Round your answer to the nearest thousandth of a cubic inch.
To calculate the mass of a piece of metal, multiply volume by density.
11. a copper ball 1.2 cm in diameter
Find the mass of each metal ball described. Assume the balls are spherical. Round your answers to the nearest tenth.
To calculate the mass of a piece of metal, multiply volume by density.
Find the mass of each metal ball described. Assume the balls are spherical. Round your answers to the nearest tenth.12. a gold ball 0.6 cm in diameter
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To calculate the mass of a piece of metal, multiply volume by density.
Find the mass of each metal ball described. Assume the balls are spherical. Round your answers to the nearest tenth.
13. an aluminum ball with radius 3 cm
To calculate the mass of a piece of metal, multiply volume by density.
Find the mass of each metal ball described. Assume the balls are spherical. Round your answers to the nearest tenth.
14. a platinum ball with radius 0.7 cm
1. 615.4 in2 3. 24871.9 ft2 5. 445865.0 ft3
7. 28938.2 yd3 9. 83280650 km2
11. 8.1 g 13. 305.2 g
Answers:
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