8.07 Volume of prisms and pyramids
Find the volume of the following prisms:
A container has the shape of a rectangular prism, with the following dimensions: 50 \text{ cm}, 80 \text{ cm}, and 20 \text{ cm}. Find its volume.
Find the volume of the following boxes in cubic centimetres.
A box is 1 \text{ m} long, 20 \text{ cm} high and 30\text{ cm} wide.
A box is 2\text{ m} long, 40\text{ cm} high and 50\text{ cm} wide.
What operation is required to convert cubic centimetres to cubic metres?
Find the volume of the following in cubic metres:
A cube with side length 150 \text{ cm}.
A rectangular prism with length 220 \text{ cm}, width 50 \text{ cm} and height 75 \text{ cm}.
A triangular prism with a length of 400 \text{ cm} and a triangular face with base length 300 \text{ cm} and height 90 \text{ cm}.
For each of the following containers, find:
The volume.
The capacity in litres.
A container shaped like a rectangular prism with dimensions 30\text{ cm} \times 80\text{ cm} \times 10\text{ cm}.
A container shaped like a rectangular prism with dimensions 50\text{ cm} \times 65\text{ cm} \times 20\text{ cm}.
Find the volume of the following pyramids. Round your answers to two decimal places where necessary.
A right pyramid has a square base with side length 24 \text{ mm} and a perpendicular height of 24 \text{ mm}. Find the volume of the pyramid.
A pyramid with a height of 7 \text{ m} has a right-angled triangular base with side lengths 6 \text{ m}, 8 \text{ m} and 10 \text{ m}. Find the volume of the pyramid.
Find the volume of a pentagonal pyramid with base area of 90 \text{ cm}^{2} and height 8 \text{ cm}.
A garden bed is 5 \text{ m} in length, 2 \text{ m} in width and 20 \text{ cm} in height.
Find the volume of soil in \text{m}^{3} that will be needed to fill up the garden bed.
Find the volume of concrete required to build the skateboard ramp shown.
Find the volume of the following tent.
Give your answer in cubic metres.
Locker A is 40 \text{ cm} long, 30 \text{ cm} wide and 160 \text{ cm} tall. Locker B is 45 \text{ cm} long, 30 \text{ cm} wide and 145 \text{ cm} tall. Which locker has the most storage?
A box of tissues is in the shape of a rectangular prism. It measures 19 \text{ cm} by 39 \text{ cm} by 11 \text{ cm}.
Find the volume of the box.
A supermarket owner wants to arrange a number of tissues boxes on a shelf such that there are no gaps between the boxes or at either end of the shelf. If the shelf at the supermarket is 95 \text{ cm} long, find the maximum number of tissues boxes that can be organised in this way.
Calculate the volume of a single sheet of paper, given that a pile of 500 sheets of paper measures 230\text{ mm} wide, 298\text{ mm} long and 30\text{ mm} tall.
Find the capacity of the following in litres:
A cubic tank with side length 29 \text{ cm}.
A rectangular swimming pool with a length of 27 \text{ m}, width of 14 \text{ m} and depth of 3 \text{ m}.
Find the capacity of the fish tank in litres:
A fish tank designed to sit in the corner of a room has the shape of a right-angled triangular prism.
If its dimensions are as shown in the image, determine the capacity of the fish tank in litres.
A medical refrigerator used to store containers has dimensions 65\text{ cm} \times 52\text{ cm} \times 26\text{ cm}. The containers have dimensions 50\text{ mm} \times 40\text{ mm} \times 20\text{ mm}.
Find the volume of one of the containers.
Find the volume of the fridge in cubic millimetres.
How many containers can be stored in the fridge?
The roof of a house is flat and measures 16 \text{ m} by 15 \text{ m} in the shape of a rectangle.
What is the area of the roof?
If a water tank collects all the water from the roof, how many litres of water would it collect if there had been 20 \text{ mm} of rain?
After the water tank has become full, a further 10 \text{ mm} of rain falls from the roof. How many litres of rainfall are not collected as a result?
The outline of a trapezium-shaped block of land is pictured on the right:
During a heavy storm, 63\text{ mm} of rain fell over the block of land.
Find the volume of water that landed on the property in litres.
A metal rectangular prism is melted down and re-cast into identical triangular prisms.
The dimensions are shown in the images below.
If all of the metal is able to be re-used, how many whole triangular prisms can be made?
If instead 7\% of the metal is wasted in the process, how many whole triangular prisms can be made?
A paperweight is in the shape of a square pyramid with dimensions as shown. The paperweight is filled with solid glass.
Find the volume of glass needed to make 3000 paperweights.
The Great Pyramid in Egypt has a square base of side length 230 \text{ m} and a vertical height of 146 \text{ m}. Find the volume of the Great Pyramid correct to one decimal place.