Surface Area of Cones

Show your work for each problem.

1.
What is the formula for the lateral (curved) surface area of a cone?
1. a)
2. b)
3. c)
4. d)
Answer:
The lateral surface area of a cone is where is the radius and is the slant height. Note that it's NOT - that would be for a cylinder.
2.
A cone has two surface parts. What are they?
1. a)Top and bottom circles
2. b)Two circular bases
3. c)Circular base and curved lateral surface
4. d)Rectangular base and lateral surface
Answer: Circular base and curved lateral surface
A cone has one circular base and a curved lateral surface that wraps from the base edge to the apex (tip). This is different from a cylinder, which has two circular bases.
3.
A cone has radius cm and slant height cm. What is the lateral surface area? Give your answer in terms of (just the coefficient).
Answer: 12
Lateral area = cm. The coefficient is 12.
4.
What is the slant height of a cone with radius and height ?
Answer: 5
. This is a 3-4-5 right triangle!
5.
Which measurement runs along the surface of the cone from the base edge to the apex?
1. a)Vertical height
2. b)Diameter
3. c)Slant height
4. d)Radius
Answer: Slant height
The slant height () runs along the surface from the base edge to the apex. The vertical height () goes straight up inside the cone. Slant height is always greater than vertical height.
6.
A cone has radius cm and slant height cm. What is the total surface area? Give your answer in terms of (just the coefficient).
Answer: 90
Total SA = cm. The coefficient is 90.
7.
A cone has radius cm and height cm. Find the total surface area in terms of .
Answer: 96pi
1. Calculate 100
2. What is the slant height ? 10
3. Calculate 16
4. What is ? (coefficient only) 96
8.
A party hat (cone) sits on your head. To calculate the cardboard needed, which surface area formula should you use?
1. a)Lateral area only:
2. b)Double the lateral area:
3. c)Total area:
4. d)Base area only:
Answer: Lateral area only:
A party hat doesn't need a base because it sits open on your head. You only need the curved lateral surface, so use .
9.
A cone has diameter cm and slant height cm. What is the lateral surface area? Give your answer in terms of (just the coefficient).
Answer: 60
First, cm. Lateral area = cm.
10.
An ice cream cone has radius cm and height cm. Find the amount of wafer material needed (lateral area only). Round to one decimal place.
Answer: 80.9
1. Calculate 106.25
2. What is the slant height ? (round to 2 decimals) 10.31
3. Calculate (round to 1 decimal) 80.9
11.
A traffic cone has a base diameter of cm and a height of cm. How much reflective material is needed to cover the entire cone? Give your answer in cm, rounded to the nearest whole number.
Answer: 2720
1. What is the radius? 15
2. Calculate 1825
3. What is the slant height ? (round to 2 decimals) 42.72
4. Calculate total SA = (round to whole number) 2720
12.
A cone has lateral surface area cm and radius cm. What is the slant height?
Answer: 13
Lateral area = . So . Dividing both sides by : cm.
13.
A conical funnel has slant height cm and lateral surface area cm. Find the height of the funnel.
Answer: 8
1. From with , solve for 6
2. Using , calculate 64
3. What is ? 8
14.
If you double both the radius and slant height of a cone, the surface area is multiplied by:
1. a)4
2. b)8
3. c)2
4. d)16
Answer: 4
Total SA = . If and : New SA = . The surface area is multiplied by 4.
15.
A cone has total surface area cm. If the slant height is twice the radius, find the radius.
Answer: 6
1. Express in terms of 2r
2. Write total SA formula with : 3r
3. So SA = . If , what is ? 36
4. What is ? 6