Worksheet: Volumes of Composite Solids

In this worksheet, we will practice finding volumes of composite solids consisting of two or more regular solids.

Q1:

A roll of paper towels has the given dimensions. Determine, to the nearest hundredth, the volume of the roll.

Q2:

Find the volume of the hexagonal prism shown in the figure.

Q3:

The figure shows the design of a swimming pool. Work out, in cubic meters, the volume of water needed to fill the swimming pool completely.

Q4:

The figure shows the design of a swimming pool. If the pool is to be filled to a point 0.5 m below the brim, work out the volume of water that would be needed in cubic meters.

Q5:

Find the volume of the given solid to the nearest tenth.

Q6:

Find, to the nearest tenth, the volume of this solid.

Q7:

Find the volume of the solid.

Q8:

The shape in the given figure consists of a cylinder with a hemisphere attached to each end. Work out its volume, giving your answer to two decimal places.

Q9:

To work out an estimate for the volume of a human body, we could model the body using a series of cylinders and spheres as seen in the given figure.

Work out the volume of the two arms in terms of 𝜋.

  • A 3 , 2 8 3 𝜋 4 8 cubic inches
  • B 3 , 2 8 3 𝜋 2 4 cubic inches
  • C 6 1 2 𝜋 cubic inches
  • D 2 4 5 𝜋 2 cubic inches
  • E 2 4 5 𝜋 4 cubic inches

Work out the volume of the two legs in terms of 𝜋.

  • A 5 , 3 3 7 𝜋 8 cubic inches
  • B 3 0 6 𝜋 cubic inches
  • C 2 4 5 𝜋 2 cubic inches
  • D 5 0 4 𝜋 cubic inches
  • E 4 4 1 𝜋 8 cubic inches

Work out the volume of the two feet in terms of 𝜋.

  • A 3 0 6 𝜋 cubic inches
  • B 6 1 2 𝜋 cubic inches
  • C 5 , 3 3 7 𝜋 8 cubic inches
  • D 6 1 2 𝜋 cubic inches
  • E 1 6 2 𝜋 cubic inches

Work out the volume of the two hands in terms of 𝜋.

  • A 3 4 3 𝜋 2 4 cubic inches
  • B 3 , 2 8 3 𝜋 4 8 cubic inches
  • C 3 , 2 8 3 𝜋 2 4 cubic inches
  • D 3 4 3 𝜋 4 8 cubic inches
  • E 2 4 5 𝜋 2 cubic inches

Work out the volume of the torso in terms of 𝜋.

  • A 5 1 2 𝜋 cubic inches
  • B 2 8 8 𝜋 cubic inches
  • C 1 , 1 5 2 𝜋 cubic inches
  • D 1 , 4 2 1 𝜋 cubic inches
  • E 1 , 2 9 6 𝜋 cubic inches

Work out the volume of the neck in terms of 𝜋.

  • A 6 4 𝜋 cubic inches
  • B 8 𝜋 cubic inches
  • C 4 𝜋 cubic inches
  • D 1 6 𝜋 cubic inches
  • E 1 2 𝜋 cubic inches

Work out the volume of the head in terms of 𝜋.

  • A 6 8 6 𝜋 3 cubic inches
  • B 5 0 0 𝜋 3 cubic inches
  • C 1 , 0 2 9 𝜋 4 cubic inches
  • D 1 , 3 7 2 𝜋 3 cubic inches
  • E 3 4 3 𝜋 1 2 cubic inches

Work out the total volume in terms of 𝜋.

  • A 2 3 , 6 6 3 𝜋 1 2 cubic inches
  • B 2 2 , 8 7 9 𝜋 1 2 cubic inches
  • C 2 4 , 1 5 7 𝜋 1 2 cubic inches
  • D 4 7 , 3 7 5 𝜋 2 4 cubic inches
  • E 5 1 , 2 9 9 𝜋 2 4 cubic inches

Q10:

By modeling the trunk of the tree as a cylinder and the head of the tree as a sphere, ignoring any air between the leaves and branches, work out an estimate for the volume of the tree seen in the given figure. Give your answer in terms of 𝜋.

  • A 1 3 9 . 5 𝜋 cubic feet
  • B 1 2 6 𝜋 cubic feet
  • C 9 7 6 . 5 𝜋 cubic feet
  • D 1 8 6 . 7 5 𝜋 cubic feet
  • E 3 4 4 . 2 5 𝜋 cubic feet

Q11:

A roll of paper towels has the given dimensions. Determine, to the nearest hundredth, the volume of the roll.

Q12:

A roll of paper towels has the given dimensions. Determine, to the nearest hundredth, the volume of the roll.

Q13:

Find the volume of the hexagonal prism shown in the figure.

Q14:

Find the volume of the hexagonal prism shown in the figure.

Q15:

Find, in terms of 𝜋, the volume of the solid generated by revolving the figure through a complete turn about 𝐴𝐵.

  • A 2 , 1 7 8 𝜋 cm3
  • B 1 , 2 1 0 𝜋 cm3
  • C 1 , 6 9 4 𝜋 cm3
  • D 7 2 6 𝜋 cm3

Q16:

Work out the volume of the trapezoidal prism shown.

  • A140 unit
  • B56 unit
  • C96 unit
  • D48 unit
  • E108 unit

Q17:

The face of the prism shown is a regular hexagon with sides of length 2 units and an area of 10.39 units2.

Work out the volume of the prism.

Work out the surface area of the prism.

Q18:

A hexagonal prism has a volume of 31 cubic inches. Suppose the dimensions are tripled. Determine the volume of the new prism.

Q19:

A cylinder of radius 7 inches and height 7 inches has a cone of the same radius and perpendicular height cut out of it.

Work out the volume of the shape formed. Give your answer in cubic inches to two decimal places.

Work out the volume of a sphere with the same radius as the cylinder. Give your answer in cubic inches to two decimal places.

Q20:

An engineer is making a concrete fence post which is formed of a cylinder with a cone at one end. The cone-shaped section needs to be 15 cm long, the cylindrical section 1.6 m long, and the diameter 11 cm. What volume of concrete does he need? Give your answer to the nearest cubic centimeter.

Q21:

Work out the volume of the shape in the given figure. Give your solution in terms of 𝜋.

  • A 5 7 6 𝜋 cubic feet
  • B 2 5 2 𝜋 cubic feet
  • C 3 9 6 𝜋 cubic feet
  • D 1 3 2 𝜋 cubic feet
  • E 2 1 6 𝜋 cubic feet

Q22:

A solid cone with a radius of 5 inches and a height of 20 inches is placed into a cylindrical tank full of water with the same height and radius.

How much water is displaced by the cone? Give your answer in cubic inches to two decimal places.

How much water is left in the cylindrical tank? Give your answer in cubic inches accurate to two decimal places.

Q23:

A shape is made up of two pyramids, each with a perpendicular height of 19 inches. They are connected by their bases which are both 10 by 10 square inches. Work out the volume of the shape, giving your answer to two decimal places.

Q24:

A triangular pyramid is placed inside a hollow circular cylinder such that the vertices of its base, which is an equilateral triangle, lie on the circumference of the base of the cylinder, and its vertex lies at the center of the upper face of the cylinder. Find the ratio between the volume of the pyramid and the volume of the cylinder in terms of 𝜋.

  • A 3 3 4 𝜋
  • B 3 2 𝜋
  • C 3 3 2 𝜋
  • D 3 1 2 𝜋
  • E 3 4 𝜋

Q25:

Determine the volume of the given solid to the nearest hundredth.

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