9.04 Volume and units
The cube shown in the diagram has a volume of 1\text{ cm}^3:
Find its volume in \text{mm}^3.
Describe how to convert a volume in cubic centimetres to get the volume in cubic metres.
Convert the following as indicated:
4\text{ m}^3 to \text{mm}^3
2.5\text{ cm}^3 to \text{mm}^3
44\,700\text{ mm}^3 to \text{cm}^3
3.61\text{ m}^3 to \text{cm}^3
9.5\text{ m}^3 to \text{mm}^3
76\,210\,000\text{ cm}^3 to \text{m}^3
120\,000\,000\text{ mm}^3 to \text{m}^3
9\,040\,000\,000\text{ mm}^3 to \text{m}^3
A rectangular prism has a base area of 28\text{ cm}^2 and a height of 7\text{ cm}. If the dimensions of the base are both doubled, find the volume of the rectangular prism.
A blue postage box has a base area of 65\text{ cm}^2 and a height of 13\text{ cm}. A red postage box has the same height but triple the base dimensions of the blue box.
Find the volume of the red postage box.
How many of the blue postage boxes can fit into the red postage box?
Noah has a jewellery box with a height of 3\text{ cm} and a base area of 14\text{ cm}^{2} . He wants to build a new jewellery box with dimensions double that of his current jewellery box.
Find the height of his new jewellery box.
Find the base area of his new jewellery box.
Find the volume of Noah's new jewellery box.
How many times larger will the volume of Noah's new jewellery box be compared to his current one?
Isabelle has a fish tank with a height of y\text{ cm} and a base area of x\text{ cm}^{2}. She wants to build a new fish tank with dimensions four times larger than that of her current fish tank.
Find the following:
The height of her new fish tank.
The base area of her new fish tank.
The volume of Isabelle's new fish tank.
How many times larger will the volume of Isabelle's new fish tank be compared to her current one?
There are two types of cylindrical juice cans available for Lyn to purchase at his local store. One has a diameter of 16\text{ cm} and a height of 18\text{ cm}, and the other has a twice the diameter and height of the smaller can.
What is the volume of the smaller can?
What is the volume of the bigger can?
How many times larger is the volume of the bigger can compared to the smaller one?
The following figure is the outline of a trapezium-shaped block of land:
Find the area of the block of land.
During a heavy storm, 41\text{ mm} of rain fell over the block of land.
Find the volume of water landed on the property in litres.
The roof of a house is flat and measures 19\text{ m} by 16\text{ m} in the shape of a rectangle.
Find 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 5\text{ mm} of rain falls from the roof. How many litres of rainfall are not collected as a result?
Locker A is 50\text{ cm} long, 35\text{ cm} wide and 180\text{ cm} tall. Locker B is 0.55\text{ m} long, 350\text{ mm} wide and 165\text{ cm} tall. Which locker has the most storage?
A special medical refrigerator used to store medical samples has dimensions 56\text{ cm} by 42\text{ cm} by 28\text{ cm}. The samples stored in small containers have dimensions 40\text{ mm} by 30\text{ mm} by 20\text{ mm}. We wish to know how many samples can fit in the fridge.
Find the volume of one of the sample containers.
Find the volume of the fridge in cubic millimetres.
How many containers can be stored in the fridge?
A box of tissues is in the shape of a rectangular prism. It measures 19\text{ cm} by 0.39\text{ m} by 11\text{ cm}.
What is 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 0.95\text{ m} long, what is the maximum number of tissues boxes that can be organised in this way?
A cylindrical spa has a radius of 1.8\text{ m} and the water is 160\text{ cm} deep. Find the volume of water in the spa in litres. Round your answer to two decimal places.
A cylindrical candle has a radius of 46\text{ mm} and a height of 0.13\text{ m}. Find the volume of the candle in cubic centimetres. Round your answer to two decimal places.
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.