What operation is required to convert cubic centimetres to cubic metres?
For each of the following containers, find:
The volume
The capacity in litres
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}.
If the radius of a cylinder is 8\text{ cm} and its height is 18\text{ cm}, find the amount of water it can hold in litres, correct to two decimal places.
A gravy boat is designed as a half-cylinder as shown. It has a diameter of 8\text{ cm} and a length of 15\text{ cm}.
Find its volume to two decimal places.
Find its capacity to two decimal places.
A cone has a radius of 4 cm, and a slant height of 12 cm. Find the following, rounding your answers to two decimal places:
The volume of the cone.
The capacity of the cone in millilitres.
Find the capacity of the ice-cream cone in millilitres.
Round your answer to one decimal place.
Consider the following hemisphere:
Find its volume. Round your answer to three decimal places.
Find its capacity in litres. 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.
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 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 planet Jupiter has a radius of 69\,911\text{ km}, and planet Mercury has a radius of 2439.7\text{ km}. How many times bigger is the volume of Jupiter than Mercury? Assume that both planets are spheres. Round your answer to one decimal place.
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.
A hanging pot plant has the shape of a hemisphere with internal diameter 20\text{ cm}.
Find the capacity of the pot. Round your answer to the nearest millilitre.
If the smallest available bag of potting mix is 3 \text{ L}, how much potting mix is left in the bag after the pot is filled? Round your answer to the nearest millilitre.
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.
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 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.
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.
A theatre serves popcorn in two different containers. The Small size popcorn comes in a cone-shaped container, and the Large size popcorn comes in a cylindrical container as shown below. Both containers have a radius of 14 \text{ cm} and a height of 30 \text{ cm}.
How many small containers must be purchased in order to have the same amount of popcorn as in one large container?
Find the volume of the small container. Round your answer to the nearest cubic centimetre.
Find the volume of the large container. Round your answer to the nearest cubic centimetre.
The cost of a small container of popcorn is \$1.30 and the cost of a large container of popcorn is \$3.50. Which is the better buy?
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.
Before 1980, Mount St. Helens was a volcano approximately in the shape of the top 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 bottom 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.
Water in a cylindrical vase reaches a height of 22\text{ cm}. Bianca pours this water into a new spherical vase.
If both vases have a radius of 17\text{ cm}, how much space will be left empty in the spherical vase once the water is poured into it? Round your answer to two decimal places.
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.
Find the volume of the following prisms:
Find the volume of the following solids, rounding your answers to one decimal place:
The following solid is 3\text{ cm} thick. Calculate the volume of the solid correct to one decimal place.
Find the volume of the composite figure shown.
Round your answer to two decimal places.
The ice-cream cones at an ice-creamery have the dimensions indicated in the diagram.
How many millilitres of icecream can fit in each cone, including the hemisphere scoop on top? Round your answer to the nearest millilitre.
The ice cream is bought in 10 L tubs. How many whole cones can be made with a single tub of ice-cream?
Double cones are served with a second hemispherical scoop of the same dimensions as the first scoop.
How many whole double cones can be made with from a 10 L tub?
A wedding cake with three tiers is 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.
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.
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.
What volume of dirt was removed to make the hole? Give your answer to the nearest cubic metre.
Find the capacity of the tank to the nearest litre.
A hollow cylindrical pipe has the dimensions shown in the figure:
Calculate the volume of the pipe, correct to two decimal places.
The pipe is made of metal where 1\text{ cm}^{3} of the metal weighs 5.7\text{ g}.
Calculate the weight of the pipe to one decimal place.
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 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.
The swimming pool shown is composed of a trapezoidal prism joined to a half cylinder:
Find the volume of the pool in cubic metres. Round your answer to three decimal places.
How many litres of water can fit in the pool? Round your answer to the nearest litre.
If the pool is filled to a height 10\text{ cm} below the top, how many litres of water are in the pool? Round your answer to the nearest litre.
After construction works at a neighbouring property, a crack opens in the bottom of the pool and water begins to leak from the pool. It is observed that the height of the surface of the water in the pool is decreasing by 7\text{ cm} each week. Find the amount of water that is leaking out each week, to the nearest litre.
Assuming that water continues to leak at this rate, find how many whole weeks it will take to empty the pool.