Find the volume of the following prisms:
What operation is required to convert cubic centimetres to cubic metres?
For each of the following containers, find:
The volume
The capacity
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 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 side length of a cube with a volume of 27 \text{ cm}^{3}.
Find the length of the rectangular prism with a volume of 162 \text{ cm}^{3}, width of 6 \text{ cm} and height of 3 \text{ cm}.
A pentagonal prism has a volume of 176.4\text{ m}^3 and a cross sectional area of 29.4\text{ m}^2. Find the height of the prism.
Consider the following prisms:
Find the volume in cubic centimetres.
Find the capacity in litres.
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.
Find the capacity of the fish tank in litres:
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 more storage room?
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.
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?
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.
This nesting box needs to have a volume of 129\,978\text{ cm}^{3}, a height of 83\text{ cm} and a width of 54\text{ cm}. Find the depth, d, of the box.
A swimming pool has the shape of a trapezoidal prism as shown in the diagram:
Find the volume of the pool in cubic metres.
If the pool is three-quarters full, find the volume of the non-filled space of the pool.
If the distance of the water level to the top of the pool is h when it is is three-quarters full, find h.
Both of the following popcorn bags are designed to carry 1152 \text{ cm}^{3} of popcorn. Assume that there is minimal wastage of space when the popcorn is packed into each bag.
Find the height, h of the following bags, in centimetres. Round your answer to two decimal places where necessary.
Bag A
Bag B
Find the surface area of the following bags:
Bag A
Bag B
Which bag should be used to reduce the amount of paper needed?
The outline of a trapezium-shaped block of land is shown:
Find the area of the block of land.
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.
The roof of a house is flat and measures 16 \text{ m} by 15 \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 10 \text{ mm} of rain falls from the roof. How many litres of rainfall are not collected as a result?
A floor plan for a granny flat is shown on the right, with measurements given in millimetres. The annual rainfall over the granny flat is 330\text{ mm}.
Find the amount of water that could fall on the granny flat over a year, in litres.
If the roof of the granny flat overhangs the edge of the floor plan by 200\text{ mm} all the way around, find the number of litres of water that could fall on the granny flat in a year.
A floor plan for a house is shown on the right, with measurements given in metres. The annual rainfall over the house is 700 millimetres.
Calculate the potential amount of water that could fall on the house over one year. Give your answer in kilolitres.
