Volume of Composite Shapes

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Show your work for each problem.

1.
A solid is a cylinder with a cone attached to its top, so the cone's circular base sits exactly on the top of the cylinder. How do you find the volume of the whole solid?
1. a)Subtract the volume of the cone from the volume of the cylinder
2. b)Use only the cylinder, because the cone is too small to count
3. c)Multiply the volume of the cylinder by the volume of the cone
4. d)Add the volume of the cylinder and the volume of the cone
2.
A cube with edges of $4$ cm is glued on top of a bigger cube with edges of $6$ cm. What is the total volume of the solid in cm³?
3.
A step block is made of two boxes. The bottom box is $8$ cm long, $4$ cm wide and $2$ cm high. A second box, $4$ cm long, $4$ cm wide and $2$ cm high, sits on top of it. Find the total volume in cm³.
4.
Which expression gives the volume of a hemisphere (half a sphere) with radius $r$ ?
1. a) $\frac{1}{3}\pi r^3$
2. b) $2\pi r^2$
3. c) $\frac{4}{3}\pi r^3$
4. d) $\frac{2}{3}\pi r^3$
5.
A small shed is a cube with edges of $2$ m. Its roof is a pyramid with a square base of $2$ m by $2$ m (the top of the cube) and a height of $1.5$ m. What is the total volume of the shed in m³?
6.
A model house is a box $6$ m long, $4$ m wide and $3$ m high, with a pyramid roof on top. The roof has the same $6$ m by $4$ m rectangular base and a height of $2$ m. Find the total volume in m³.
7.
A wooden cube has edges of $10$ cm. A small cube with edges of $4$ cm is cut out of one corner. What volume of wood is left, in cm³?
8.
A rocket model is $15$ cm tall: a cylinder with radius $2$ cm and height $9$ cm, with a cone of radius $2$ cm and height $6$ cm on top. Which expression gives its volume?
1. a) $\pi \cdot 2^2 \cdot 9 + \frac{1}{3}\pi \cdot 2^2 \cdot 6$
2. b) $\pi \cdot 2^2 \cdot 15$
3. c) $\pi \cdot 2^2 \cdot 9 + \pi \cdot 2^2 \cdot 6$
4. d) $\pi \cdot 2^2 \cdot 15 + \frac{1}{3}\pi \cdot 2^2 \cdot 6$
9.
A crayon is a cylinder with radius $1$ cm and length $9$ cm, with a cone-shaped tip of radius $1$ cm and height $3$ cm. Use $\pi \approx 3.14$ to find its volume in cm³.
10.
An ice cream cone has radius $3$ cm and height $8$ cm and is completely filled. A hemisphere-shaped scoop of radius $3$ cm sits on top. The total volume of ice cream is $k\pi$ cm³. What is $k$ ?
11.
A capsule-shaped container is a cylinder with radius $3$ cm and length $12$ cm, with a hemisphere of radius $3$ cm on each end. Use $\pi \approx 3.14$ and round the total volume to the nearest whole cm³.
12.
A wooden block is $10$ cm long, $10$ cm wide and $6$ cm high. A cylindrical hole with radius $2$ cm is drilled straight down through its whole $6$ cm height. Using $\pi \approx 3.14$ , what volume of wood is left, rounded to the nearest tenth?
1. a)675.4 cm³
2. b)524.6 cm³
3. c)600 cm³
4. d)298.6 cm³
13.
A silo is a cylinder with radius $2$ m and height $8$ m, with a hemisphere-shaped roof of radius $2$ m. Use $\pi \approx 3.14$ . What is the volume of the silo in m³, rounded to the nearest whole number?
14.
A solid cylinder has radius $6$ cm and height $10$ cm. A cone with the same base (radius $6$ cm) and the same height ( $10$ cm) is hollowed out of it, with its tip pointing down inside the cylinder. Use $\pi \approx 3.14$ to find the volume of material that is left, in cm³.
15.
A metal pipe is $50$ cm long. Its outer radius is $6$ cm and its inner radius (the hole) is $5$ cm. Which expression gives the volume of metal in the pipe?
1. a) $\pi (6 - 5)^2 \cdot 50$
2. b) $\pi \cdot 6^2 \cdot 50$
3. c) $\pi \cdot 6^2 \cdot 50 + \pi \cdot 5^2 \cdot 50$
4. d) $\pi (6^2 - 5^2) \cdot 50$
16.
A concrete drain pipe is $200$ cm long. Its outer radius is $10$ cm and its inner radius is $8$ cm. Use $\pi \approx 3.14$ to find how many liters of concrete it contains ( $1$ L $= 1000$ cm³).
17.
A fish tank is a box $30$ cm long, $20$ cm wide and $20$ cm high. A solid decoration shaped like a cylinder, with radius $5$ cm and height $20$ cm, stands upright inside it. Using $\pi \approx 3.14$ , how many liters of water are needed to fill the rest of the tank? ( $1$ L $= 1000$ cm³)
18.
A solid is a cylinder with a hemisphere on top, both with radius $3$ cm. Its total volume is $90\pi$ cm³. How tall is the cylinder part? (Work in terms of $\pi$ .)