Volume of Cones

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Show your work for each problem.

1.
Which formula gives the volume of a cone with radius $r$ and height $h$ ?
1. a) $V = \frac{4}{3}\pi r^3$
2. b) $V = \frac{1}{3}\pi r^2 h$
3. c) $V = 2\pi r h$
4. d) $V = \pi r^2 h$
2.
A cylinder has a volume of 90 cm³. A cone has the same base and the same height. What is the volume of the cone in cm³?
3.
A cone has radius 3 cm and height 5 cm. Its volume is $\square\,\pi$ cm³. What number goes in the box?
4.
A traffic cone has a base with a diameter of 10 cm. Which value do you put in for $r$ in the volume formula?
1. a)20 cm
2. b)2.5 cm
3. c)5 cm
4. d)10 cm
5.
Find the volume of a cone with radius 2 cm and height 6 cm. Use $\pi \approx 3.14$ and give the answer in cm³ (no rounding needed).
6.
A party hat is a cone with radius 3 cm and height 4 cm. Its volume is $\square\,\pi$ cm³. Find the number in the box.
7.
A cone has a radius of 6 cm and a slant height of 10 cm. What is its perpendicular height?
1. a)8 cm
2. b)4 cm
3. c)10 cm
4. d)16 cm
8.
A pile of gravel is a cone with a diameter of 4 m and a height of 3 m. How many m³ of gravel are in the pile? Use $\pi \approx 3.14$ and round to the nearest hundredth.
9.
An ice cream cone has a diameter of 6 cm and a height of 11 cm. Find its volume with $\pi \approx 3.14$ , rounded to the nearest tenth of a cm³.
10.
You double the height of a cone and keep the radius the same. What happens to its volume?
1. a)It triples
2. b)It stays the same
3. c)It doubles
4. d)It becomes 4 times as large
11.
A cone has a volume of $12\pi$ cm³ and a radius of 3 cm. What is its height in cm?
12.
A kitchen funnel is a cone with radius 5 cm and height 9 cm. How many cm³ does it hold when full? Use $\pi \approx 3.14$ (no rounding needed).
13.
A cylinder and a cone both have radius 4 cm and height 6 cm. The cylinder holds $\square\,\pi$ cm³ more than the cone. Find the number in the box.
14.
You double the radius of a cone and keep the height the same. How does the new volume compare with the old one?
1. a)8 times as large
2. b)4 times as large
3. c)2 times as large
4. d)3 times as large
15.
A cone has radius 5 cm and slant height 13 cm. Its volume is $\square\,\pi$ cm³. What number goes in the box?
16.
A cone has a volume of 301.44 cm³ and a height of 8 cm. Find its radius in cm. Use $\pi \approx 3.14$ .
17.
A cone-shaped tent has a radius of 9 dm and a slant height of 15 dm. Find its volume in dm³. Use $\pi \approx 3.14$ (no rounding needed).
18.
Cone-shaped paper cups have radius 3 cm and height 10 cm. How many full cups do you need to fill a 1 liter (1000 cm³) jug completely? Use $\pi \approx 3.14$ .