Find the volume of the following prisms:
A triangular tunnel is made through a rectangular prism as shown in the figure. Find the volume of the solid formed.
The larger prism has had two identical holes carved out of it, each of which is a rectangular prism. Find the volume of the remaining solid, correct to two decimal places. All measurements are in metres.
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.
A floor plan for a house is shown on the right, with measurements given in millimetres. The annual rainfall over the house is 330\text{ mm}.
Find the amount of water that could fall on the house over a year, in litres.
If the roof of the house 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 house in a year.
Find the volume of the following solids, correct to one decimal place:
Find the volume of the composite solid shown, correct to two decimal places. Note that the two rectangular prisms are identical.
A wedding cake with three tiers as shown. The layers have radii of 51\text{ cm}, 55\text{ cm} and 59\text{ cm}.
If each layer is 20\text{ cm} high, calculate the total volume of the cake in cubic metres. Round your answer to two decimal places.
The following solid was created by cutting a cylindrical hole through a cube, such that the cylinder's diameter is equal to the cube's side length.
Calculate the volume of the solid, correct to two decimal places.
A hole is drilled through a rectangular box forming the solid shown.
Find the volume of the solid, correct to two decimal places.
Two holes are drilled through a rectangular prism as shown.
Calculate the volume of the solid, correct to one decimal place.
A 13 \text{ cm} concrete cylindrical pipe has an outer radius of 6 \text{ cm} and an inner radius of 4 \text{ cm} as shown:
Find the volume of concrete required to make the pipe, correct to two decimal places.
A cylinder is hollowed out by a hole of radius 5 \text{ cm}.
Find the volume of the remaining figure, correct to two decimal places.
Consider the following cylindrical pipe:
Calculate the volume of the pipe, correct to two decimal places.
The pipe is made of a particularly strong metal. Calculate the weight of the pipe if 1 \text{ cm}^{3} of the metal weighs 5.7 \text{ g}, correct to one decimal place.
A small square pyramid of height 4 \text{ cm} was removed from the top of a large square pyramid of height 8 \text{ cm} forming the solid shown.
Find the exact volume of the solid.
A weight is constructed by removing the top 38 \text{ cm} from a 57 \text{ cm} tall pyramid with a square base of side length 45 \text{ cm}.
Find the volume of the original pyramid.
Calculate the side length of the square on top of the weight.
Calculate the volume of the removed part of the pyramid.
Calculate the volume of the weight.
A pyramid has been removed from a rectangular prism, as shown. Find the volume of the remaining solid.
Find the volume of the following hemisphere, correct to three decimal places:
Consider the following hemisphere:
Find the volume of the hemisphere, rounded to three decimal places.
What is the capacity in litres? Round your answer to the nearest litre.
A cone with a height of 9 \text{ cm} and diameter of 3 \text{ cm} is sliced exactly in half. Find the volume of half of the cone, correct to two decimal places.
Before 1980, Mount St. Helens was a volcano approximately in the shape of the first cone below:
What was the volume of the mountain, in cubic kilometres? Round your answer to two decimal places.
The tip of the mountain was in the shape of the second cone shown.
Find the volume of the tip in cubic kilometres. Round your answer to two decimal places.
In 1980, Mount St. Helens erupted and the tip was destroyed.
Find the volume of the remaining mountain, in cubic kilometres. Round your answer to two decimal places.
Consider the silo shown in the diagram, which is used to store wheat for farms.
If the density of wheat is 760 \text{ kg} per \text{m}^3, how many kilograms of wheat will fit in the grain silo?
Round your answer to one decimal place.
