Find the volume of the following prisms:
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 pentagonal prism.
A triangular tunnel is made through a rectangular prism as shown in the figure below. 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.
Find the volume of the following solids, correct to one decimal place:
Find the volume of a cylinder, correct to one decimal place if:
Its radius is 6 \text{ cm} and height is 15 \text{ cm.}
Its diameter is 2 \text{ cm} and height is 19 \text{ cm.}
There are two types of cylindrical soup cans available for Bob to purchase at his local store. The first has a diameter of 16 \text{ cm} and a height of 18 \text{ cm}, and the second has a diameter of 18 \text{ cm} and a height of 16 \text{ cm}. State which type of can holds more soup, the first can or the second can.
Two holes are drilled through a rectangular prism as shown. Calculate the volume of the solid, correct to one decimal place.
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.
Find the volume of the following pyramids:
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 below. Find the exact volume of the solid.
A right square pyramid has a height of 24 \text{ cm} and a volume 2592 \text{ cm}^{3}. Find its base length.
A pyramid has been removed from a rectangular prism, as shown. Find the volume of the remaining solid.
Find the volume of the following spheres. Round your answers to two decimal places.
Find the volume of the following hemisphere, correct to three decimal places:
Find the radius, r, of the following spheres. Round your answers to two decimal places.
A sphere with a volume of 72 \pi \text{ cm}^{3}
A ball with a volume of 24\,449.024 \text{ units}^3
Find the volume of the following hemisphere. Round your answer to three decimal places.
Consider the following hemisphere:
Find the volume of the hemisphere in cubic centimetres. Round your answer to three decimal places.
Find its capacity in litres.
Find the volume of the following solid. Round your answer to two decimal places.
Find the volume of the fish tank:
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?
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.
The Great Pyramid in Egypt has a square base with side length 230 \text{ m} and a vertical height of 146 \text{ m}. Find the volume of the Great Pyramid.
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.
Three spheres of radius 4\text{ cm} fit perfectly inside a cylindrical tube so that the height of the three spheres is equal to the height of the tube, and the width of each sphere equals the width of the tube.
Find the total volume of the three spheres. Round your answer to one decimal place.
Find the volume of the tube. Round your answer to one decimal place.
Calculate the percentage of the space inside the tube that is not taken up by the spheres. Round your answer to the nearest whole number.
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 concrete block is a square prism with dimensions 20 \text{ m} \times 20 \text{ m} \times 4\text{ m}. A cylindrical hole of diameter 4 m is drilled through the square face through the length of the prism
Calculate the volume of the concrete block to the nearest \text{ m}^{3}.
Calculate the percentage of concrete that was removed to make the hole. Round your answer correct to one decimal place.
A cylindrical tank with diameter of 3\text{ m} is placed in a 2 \text{ m} deep circular hole so that there is a gap of 40\text{ cm} between the side of the tank and the hole. The top of the tank is level with the ground.
Calculate the volume of dirt that was removed to make the hole. Round your answer to the nearest metre cubed.
A wedding cake with three tiers is shown. The layers have radii of 51\text{ cm}, 55\text{ cm} and 59\text{ cm} and 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 swimming pool shown is composed of a trapezoidal prism joined to a half cylinder.
Find the volume of the pool in cubic metres, correct to one decimal place.
This concrete weight is a truncated right pyramid. Its square base has side length b, the square top face has side length a, and the vertical height of the truncated pyramid is h. The vertical height of the original pyramid was H.
Form a simplified expression for the volume of the truncated pyramid in terms of h, a and b.
