Volume of Pyramids

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Show your work for each problem.

1.
Which formula gives the volume of any pyramid? ( $B$ = base area, $h$ = height)
1. a) $V = \frac{1}{3}Bh$
2. b) $V = \frac{1}{2}Bh$
3. c) $V = 3Bh$
4. d) $V = Bh$
2.
A pyramid has a square base with sides of $3$ m and a height of $5$ m. What is its volume in m³?
3.
Find the volume of a square pyramid with base sides of $5$ cm and a height of $12$ cm.
4.
A prism and a pyramid have the same base and the same height. The prism has a volume of $90$ cm³. What is the volume of the pyramid?
1. a)45 cm³
2. b)90 cm³
3. c)30 cm³
4. d)270 cm³
5.
A pyramid has a base area of $24$ cm² and a height of $7$ cm. What is its volume in cm³?
6.
A pyramid has a rectangular base of $9$ m by $4$ m and a height of $5$ m. Find its volume.
7.
In $V = \frac{1}{3}Bh$ , which length is $h$ ?
1. a)The perpendicular distance from the apex to the base
2. b)The length of a base edge
3. c)The slant height of a triangular face
4. d)The length of an edge from the apex to a corner
8.
A pyramid has a rectangular base of $7$ cm by $6$ cm and a height of $10$ cm. What is its volume in cm³?
9.
The base of a pyramid is a right triangle with legs of $6$ cm and $8$ cm. The pyramid is $15$ cm tall. Find its volume.
10.
A square pyramid has base sides of $4$ cm and a height of $6$ cm. Which calculation gives its volume?
1. a) $\frac{1}{2} \times 4^2 \times 6$
2. b) $\frac{1}{3} \times 4^2 \times 6$
3. c) $\frac{1}{3} \times 4 \times 6$
4. d) $4^2 \times 6$
11.
The base of a pyramid is a triangle with a base of $10$ cm and a height of $6$ cm. The pyramid is $8$ cm tall. What is its volume in cm³?
12.
A pyramid with a rectangular base of $8$ cm by $5$ cm has a volume of $120$ cm³. How tall is it?
13.
A box (rectangular prism) has a square base of $6$ cm by $6$ cm and is $10$ cm tall. A hollow pyramid has the same base and height. How many full pyramids of sand fill the box?
14.
You double the side of a square pyramid's base and keep the height the same. By how much is the volume multiplied?
1. a)×8
2. b)×3
3. c)×4
4. d)×2
15.
A square pyramid has a volume of $200$ cm³ and a height of $6$ cm. How long is one side of its base, in cm?
16.
A square pyramid has base sides of $16$ cm and a slant height of $17$ cm. Find its volume.
17.
A large group tent is a square pyramid. Its floor has sides of $6$ m and the slant height of each face is $5$ m. How much air is inside?
18.
A glass paperweight is a square pyramid with a volume of $384$ cm³ and a height of $8$ cm. How long is one side of its base, in cm?