Surface Area of Spheres

Show your work for each problem.

1.
What is the formula for the surface area of a sphere?
1. a)
2. b)
3. c)
4. d)
Answer:
is the surface area formula. is volume, is circumference, and is circle area.
2.
A sphere has a radius of cm. What is ?
Answer: 9
. This is the first step in calculating surface area.
3.
If a sphere has diameter cm, what is the radius?
1. a) cm
2. b) cm
3. c) cm
4. d) cm
Answer: cm
Radius cm. Always convert diameter to radius before using the formula.
4.
A sphere has radius cm. What is in terms of ? (Answer as a number followed by pi, e.g., 16pi)
Answer: 4pi
cm². When , the surface area is simply .
5.
Calculate the surface area of a sphere with radius cm. Give the exact answer in terms of .
Answer: 16pi
1. What is the formula for surface area? 4 pi r^2
2. What is when ? 4
3. What is ? 16
4. So the surface area is? 16pi
6.
A sphere has radius cm. What is its surface area in terms of ? (Answer as number followed by pi)
Answer: 100pi
cm²
7.
A sphere has diameter cm. Calculate its surface area in terms of .
Answer: 64pi
1. What is the radius if diameter is 8 cm? 4
2. What is ? 16
3. What is ? 64
4. The surface area is? 64pi
8.
A sphere has surface area cm². What is its radius?
1. a) cm
2. b) cm
3. c) cm
4. d) cm
Answer: cm
→ → → cm
9.
Calculate the surface area of a sphere with radius cm. Round to the nearest whole number. (Use )
Answer: 616
cm²
10.
A basketball has a diameter of cm. What is its surface area? Round to the nearest whole number. (Use )
Answer: 1809
1. What is the radius? 12
2. What is ? 144
3. What is ? 12.56
4. What is ? 1809
11.
If you double the radius of a sphere, what happens to its surface area?
1. a)It stays the same
2. b)It quadruples (×4)
3. c)It increases 8 times (×8)
4. d)It doubles (×2)
Answer: It quadruples (×4)
If becomes : . This is 4 times the original .
12.
A sphere has a surface area of cm². Find its radius.
Answer: 8
1. Set up the equation: . Divide both sides by . What do you get? 256 = 4r^2
2. Divide both sides by 4. What is ? 64
3. Take the square root. What is ? 8
13.
A spherical tank needs m² of steel for its surface. What is the radius? (Use )
Answer: 4
→ → m
14.
Earth has a radius of approximately km. Calculate its surface area in scientific notation. (Use )
Answer: 5.1 x 10^8
1. What is ? (Round to millions) 40590000
2. What is ? 12.56
3. Multiply: . About how many million km²? 510
4. Write in scientific notation: 5.1 x 10^8
15.
Sphere A has radius cm and Sphere B has radius cm. What is the ratio of their surface areas (A:B)?
1. a)
2. b)
3. c)
4. d)
Answer:
. . Ratio = . Since B has double the radius, it has times the surface area.
16.
A hemisphere (half a sphere) has a flat circular base and a curved surface. If the radius is cm, what is the total surface area? (Include both the curved part and the flat base)
Answer: 108pi
1. What is the curved surface area of a hemisphere? (Half of a full sphere) 2 pi r^2
2. Calculate the curved surface: 72pi
3. What is the area of the circular base? () 36pi
4. Total surface area = curved + base: 108pi