# Volume - practice problems

Volume is the measure of the space that a body fills or occupies. The basic SI unit of volume is the cubic meter. It is the volume of a cube with an edge of one meter, i.e., 1 m x 1 m x 1 m. Significant another unit is 1 l (one liter), 1 m^{3}= 1000 l applies. One hectoliter (1 hl) is 100 liters.

Volume is always the third power of length. Or volume = area times length. For example, the volume of the cube is a

^{3}, and the prism's volume is S*h (the area of the base times the height). The volume of rotating bodies (sphere, cone) can be derived in high school by integration. The pyramid's volume is always 1/3 of the prism's volume. We calculate the volume of the truncated bodies either with a formula or simply by subtracting the volumes of the two bodies.

#### Number of problems found: 2389

- A tank 2

A tank can be filled by a pipe A in 3 hours and by pipe B in 5 hours. When the tank is full, it can be drained by pipe C in 4 hours. If the tank is initially empty and all three pipes are open, how many hours will it take to fill up the tank? - A bottle 3

A bottle of water contains 16.9 ounces. How many total ounces are there in 24 bottles? - The petrol tank

Tinny's car's petrol tank was full. He drove around the city and used 1/4 of the petrol. What fraction of the petrol was left? - Full tank 2

Robert has a full tank of petrol. He drove to Manly and used 1/8 of a tank and then to Gosford using another 4/8 of a tank. What fraction of a tank of petrol has he used?

- The cuboid 2

If the areas of three adjacent faces of a cuboid are 6,10,22 respectively then find the volume of the cuboid. - The frustum

A frustum of a pyramid is 4 cm at the top and 7 cm at the bottom square, and it's 6 cm high. Calculate the volume of the frustum. - A swimming 2

A swimming pool had 2.5 million liters of water in it. Some water evaporated, and then the pool only had 2 million liters of water in it. What percent of the water evaporated? - Milk mixture

In a container, milk and water are 7:5. If 15 L water is added, the ratio becomes 7:8. Find the quantity of water in the new mixture. - Two pipes 3

Two pipes, A and B, can fill a tank in 15 minutes and 20 minutes, respectively. Both pipes are opened together. After 4 minutes, pipe A is turned off.What is the total time required to fill the tank?

- A conical

A conical tent can accommodate 11 people. Each person needs 4 m² of space on the ground and 20 m³ of air to breathe. Find the height of the tent. - Milk with water

How many liters of water are to be mixed in 12 liters of milk costing Rs 40 per liter so that it can be sold at Rs 32 per liter? - Melting 3 cubes

The sides of the three metal cubes are 30 cm, 40 cm, and 50 cm, respectively. Find the side of the new cube formed by melting these cubes together. - Water tank 12

A rectangular water tank is 5 m high, 3 m long, and 2 m wide. How many liters of water can it hold? - Cylinders and cube

How many cylinders of radius 20 cms and height 0.7 metres can be formed by melting a cube of 2.2 metres sides?

- Petrol, fuel

In a car meter shows that it has kept oil 1/5 of its fuel capacity. When 22 liters of petrol is filled the meter went on 3/4 of its capacity. Find the capacity of the car. - Two syrups

There are two pots of mixture of syrup and water having ratios 3:2 & 4:5 respectively. What quantity of solution of 1st pot is to be mixed with 3 litre of 2nd pot to get a new mixture where both syrup and water will be same? - A provision

John had provisions for a certain number of days. After 10 days 1/5 of the men desert and he is found that the provisions will now last just as long as before. How long was that? - Glass cleaner

A 2-pint bottle of glass cleaner costs $13.44. What is the price per fluid ounce? - Plasticine cuboid

Paul makes a cuboid of plasticine with sides 5 cm, 2 cm, and 5 cm. How many such cuboids will he need to form a cube?

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