Worksheet: Volumes of Composite Prisms

In this worksheet, we will practice finding volumes of composite prisms.

Q1:

Benjamin made a cardboard house at school. The lower part of the house is a rectangular prism and the upper part a triangular prism. Find the volume of the house.

Q2:

The solid shown is a rectangular prism with a triangular prism cut out along its length. Work out the volume of the solid.

  • A210 unit3
  • B84 unit3
  • C126 unit3
  • D168 unit3
  • E198 unit3

Q3:

The solid shown is formed from two rectangular prisms. Work out the volume of the solid.

  • A800 unit
  • B1,200 unit
  • C880 unit
  • D720 unit
  • E1,040 unit

Q4:

A prism has volume 218.12 cubic meters and a base with area 13.3 square meters. Write an equation that can be used to find the height , then find the height of this prism.

  • A13.3=218.12, =204.8m
  • B218.12=13.3, =204.8m
  • C13.3=109.06, =204.8m
  • D218.12=13.3, =16.4m
  • E13.3=218.12, =16.4m

Q5:

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

Q6:

The solid shown is formed from two congruent triangular prisms placed together with a rectangular prism cut out along its length. Work out the volume of the solid.

Q7:

Work out the volume of the prism shown.

  • A60 unit
  • B48 unit
  • C120 unit
  • D180 unit
  • E96 unit

Q8:

Work out the volume of the trapezoidal prism shown.

  • A216 unit
  • B48 unit
  • C108 unit
  • D96 unit
  • E72 unit

Q9:

A sphere with a volume of 2,304𝜋 cm3 is placed inside a cube. Given that it touches all six of the cube’s faces, find the volume of the cube.

Q10:

Find the edge length of the smallest cube in which a sphere of volume 2,304𝜋 cm3 fits.

Q11:

David makes an ice cream cone with two spherical scoops of ice cream. Before he has time to eat the ice cream it melts and fills the cone up to the very top. Given that the cone has an internal height of 14 cm and an internal radius of 3 cm, what is the radius of a scoop of ice cream?

  • A218 cm
  • B632 cm
  • C3272 cm
  • D372 cm
  • E634 cm

Q12:

A cylindrical tank with a radius of 3 feet is partially filled with water. A spherical ball with a radius of 2 feet is dropped into the tank. Assuming that the sphere is completely submerged and the cylindrical tank does not overflow, find the height, , by which the water level rises. Give your answer to two decimal places.

Q13:

A cube has a volume of 9,261 cubic inches. Find, to the nearest tenth, the volume of the circumscribed sphere of the cube.

Q14:

Calculate the volume of the figure.

Q15:

Work out the volume of the composite prism shown.

  • A72 unit
  • B128 unit
  • C64 unit
  • D112 unit
  • E56 unit

Q16:

Work out the volume of the composite prism shown.

  • A42 unit
  • B48 unit
  • C36 unit
  • D40 unit
  • E60 unit

Q17:

The solid shown is formed from a rectangular prism and a trapezoidal prism. Calculate the volume of this solid.

  • A288 unit3
  • B336 unit3
  • C384 unit3
  • D324 unit3
  • E360 unit3

Q18:

An antique is kept sealed in a cube-shaped box which has an external length of 4 cm. To transport it, the box is placed in a cube-shaped crate with an internal edge length of 38 cm, and the empty space around it is filled with packing foam. Find the volume of the packing foam.

Q19:

A cubic container has an inner edge length of 28 cm. It is filled with water, which rises 6 cm when a metal object is placed inside. Find the volume of the object.

Q20:

A rectangular-prism-shaped box with a volume of 18 cubic inches is filled with small cubes of side lengths equal to 14 of an inch. Determine the number of small cubes.

Q21:

A rectangular shaped hole has been cut all the way through this rectangular prism as shown. Work out the volume of the remaining solid.

  • A297 unit
  • B276 unit
  • C108 unit
  • D234 unit
  • E162 unit

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