Surface Area of Cylinders

Show your work for each problem.

1.
What is the formula for the total surface area of a cylinder?
1. a)
2. b)
3. c)
4. d)
Answer:
The total surface area formula is : for the two circular bases, and for the lateral surface.
2.
A cylinder has radius cm and height cm. What is the area of one circular base? Use .
1. a) cm²
2. b) cm²
3. c) cm²
4. d) cm²
Answer: cm²
Area of one base = cm².
3.
A cylinder has radius cm. What is the area of both circular bases combined? Use .
Answer: 157
Both bases = cm².
4.
Find the lateral surface area of a cylinder with radius cm and height cm. Use .
Answer: 150.72
Lateral area = cm².
5.
If you unroll the lateral surface of a cylinder, what shape do you get?
1. a)Rectangle
2. b)Circle
3. c)Triangle
4. d)Square
Answer: Rectangle
The lateral surface unrolls into a rectangle with width equal to the circumference () and height equal to the cylinder's height ().
6.
Find the total surface area of a cylinder with radius cm and height cm. Use .
Answer: 188.4
1. Calculate the area of both bases () 56.52
2. Calculate the lateral surface area () 131.88
3. Add both parts for total surface area 188.4
7.
A soup can has diameter cm and height cm. Find the total surface area. Use .
Answer: 401.92
Radius = cm. SA = cm².
8.
Use the factored formula to find the surface area of a cylinder with radius m and height m. Use .
Answer: 408.2
1. Calculate 13
2. Calculate 31.4
3. Multiply to get total surface area 408.2
9.
A label wraps around a cylindrical can. Which formula gives the area of the label?
1. a)
2. b)
3. c)
4. d)
Answer:
A label only covers the lateral (curved) surface, so we use the lateral surface area formula: .
10.
A pipe has radius cm and length cm. What is the outer surface area (lateral only)? Use .
Answer: 942
1. What formula do we use for lateral area only? 2 pi r h
2. Calculate 18.84
3. Multiply by the length (height) of 50 942
11.
If a cylinder has lateral surface area cm² and radius cm, what is its height? Use .
Answer: 10
cm.
12.
A cylinder has total surface area cm² and height cm. Find the radius. Use .
Answer: 5
1. Write the formula and substitute 282.6 = 6.28r(r + 4)
2. What is if ? 9
3. Check: 282.6
13.
A paint can has radius cm and height cm. How many square centimeters of metal are used to make the can? Use .
Answer: 967.12
cm².
14.
A storage tank has surface area m² and radius m. If you know both bases contribute m², find the height.
Answer: 16
1. Find the lateral surface area (total SA - base areas) 401.92
2. Calculate (the circumference) 25.12
3. Divide lateral area by circumference to get height 16
15.
If you double the radius of a cylinder while keeping the height the same, how does the lateral surface area change?
1. a)It doubles
2. b)It quadruples
3. c)It stays the same
4. d)It triples
Answer: It doubles
Lateral area = . If becomes , the new lateral area is , which is double the original.
16.
A company needs to print labels for 200 cans. Each can has radius cm and height cm. What total area of paper is needed? Use .
Answer: 37680
1. What formula do we use for label area? 2 pi r h
2. Calculate one label area 188.4
3. Multiply by 200 for total area 37680