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1 12.6 surface area and volume of spheres ink.notebook Page 171 Page Surface Area and Volume of Spheres Page 173 Page 174 Page 175 1
2 Lesson Objectives Standards Lesson Notes Lesson Objectives Standards Lesson Notes 12.6 Surface Area and Volume of Spheres After this lesson, you should be able to successfully find the surface area and volume of spheres. Press the tabs to view details. Press the tabs to view details. Lesson Objectives Standards Lesson Notes G.MG.1 Use geometric shapes, their measures, and their properties to describe objects. G.GMD.4 Identify the shapes of two dimensional crosssections of three dimensional objects, and identify three dimensional objects generated by rotations of two dimensional 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. 2
3 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 πr 2. The total surface area of the sphere is four times the area of a great circle. Surface Area of a Sphere If a sphere has a surface area of SA square units and a radius of r units, then SA = 4πr 2. 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. 2. Find the surface area of 3. Find the surface area of the sphere. Round to the the sphere. Round to the SA = 4πr 2 3
4 12.6 surface area and volume of spheres ink.notebook 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
5 Find the volume of each sphere or hemisphere. Round to the 7. hemisphere: radius 5 in. 8. sphere: circumference of great circle 25 ft Find the volume of each sphere or hemisphere. Round to the 9. hemisphere: area of great circle 50 m 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? 5
6 12.6 surface area and volume of spheres ink.notebook 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 6
7 On the Worksheet HOMEWORK 12.6 Practice WS Surface Areas and Volumes of Spheres Find the surface area of each sphere. Round to the Find the surface area of each sphere. Round to the 3. 7
8 Find the volume of each sphere or hemisphere. Round to the Find the volume of each sphere or hemisphere. Round to the 6. Find the volume of each sphere or hemisphere. Round to the 7. hemisphere: diameter = 48 yd Find the volume of each sphere or hemisphere. Round to the 8. sphere: circumference 26 m 8
9 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 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. 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 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 12. a gold ball 0.6 cm in diameter 9
10 To calculate the mass of a piece of metal, multiply volume by density. 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 13. an aluminum ball with radius 3 cm Find the mass of each metal ball described. Assume the balls are spherical. Round your answers to the 14. a platinum ball with radius 0.7 cm Answers: in ft ft yd km g g 10
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Name: Date: The masses of the various objects can be determined using the balance. Measure the masses and record the numbers in Table 7.2.
Name: Date: 7 Density 7.1 Introduction In this lab we will consider how to determine the average density of irregular shapes and what that density can tell us about the internal composition and structure