7.02 Volume of prisms and cylinders
For each of the following prisms:
State the shape of the prism's base.
Find the area of the prism's base.
Find the volume of the prism.
Find the volume of the following prisms:
A prism has a volume of 880 \text{ cm}^3. If it has a height of 11 \text{ cm}, find the base area of the prism.
A prism has a volume of 1080 \text{ cm}^3. If it has a base area of 120 \text{ cm}^2, find the height of the prism.
Find the volume of the following solids, rounding your answers to one decimal place:
There are two types of cylindrical soup cans available for Ray 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 diameter of 18 \text{ cm} and a height of 16 \text{ cm} . Which type of can holds more soup?
Jack's mother told him to drink 3 large bottles of water each day. She gave him a cylindrical bottle with height 17\text{ cm} and radius 5\text{ cm}.
Find the volume of the bottle. Round your answer to two decimal places.
Assuming that he drinks 3 full bottles as his mother suggested, calculate the volume of water Jack drinks each day. Round your answer to two decimal places.
If Jack follows this drinking routine for a week, how many litres of water would he drink altogether? Round your answer to the nearest litre.
Find the capacity of the fish tank in litres:
A cylindrical swimming pool has a diameter of 5\text{ m} and a depth of 1.8\text{ m}.
How many litres of water can the pool contain? Round your answer to the nearest litre.
Express this amount of water in kilolitres.
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.
A rectangular swimming pool has a length of 27\text{ m}, width of 14\text{ m} and depth of 3\text{ m}.
Find the capacity of the swimming pool in litres.
The roof of a cottage has the shape of a triangular prism with the dimensions shown below.
Find the volume of the roof.
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.
Find the volume of the following tent in cubic metres:
A metal rectangular prism is melted down and re-cast into identical triangular prisms as shown in the images below:
If all of the metal is able to be re-used, calculate the number of whole triangular prisms that can be made.
If 7\% of the metal is wasted in the process, calculate the number of whole triangular prisms that can be made.
The roof of a house is flat and measures 16\text{ m} by 11 \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?
The outline of a paddy field used to grow rice is pictured on the right:
Find the area of the rice paddy.
Throughout the monsoon season, the rice paddy receives 16 \text{ cm} of rain. What volume of water, in cubic metres, has fallen on the paddy?
The image on the right shows the outline of a construction site for the foundations of a large office building:
Find the area of the construction site.
Prolonged rainstorms bring 0.21 \text{ m} of rain to the region and the foundations of the building are flooded. Determine the volume of water in the construction site.
A floor plan for a house is shown on the right, with measurements given in metres. The annual rainfall over the house is 700 \text{ mm}.
Calculate the potential amount of water that could fall on the house over one year. Give your answer in kilolitres.
