Geo 12.6 Surface Area and Volume of Spheres
Name ____________________________
Learning Objective: After this lesson, you should be able to successfully find the surface area and volume
of spheres.
Standard:
G.MG.1 Use geometric shapes, their measures, and their properties to describe objects.
G.GMD.4 Identify the shapes of two-dimensional cross-sections 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.
Find the surface area of each sphere. Round to the nearest tenth.
1.
2.
3.
Find the volume of each sphere or hemisphere. Round to the nearest tenth.
4.
7. hemisphere: diameter = 48 yd
5.
6.
8. sphere: circumference ≈ 26 m
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 2
1
inches in diameter. What is the total volume
4
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.
Find the mass of each metal ball described. Assume the balls are spherical. Round your answers to the
nearest tenth.
11. a copper ball 1.2 cm in diameter
12. a gold ball 0.6 cm in diameter
13. an aluminum ball with radius 3 cm
14. a platinum ball with radius 0.7 cm
Answers: 1. 615.4 in2
11. 8.1 g
13. 305.2 g
3. 24871.9 ft2
5. 445865.0 ft3
7. 28938.2 yd3
9. 83280650 km2