Volume and Capacity

Q.

A hemispherical tank has inner radius of 2.8 m. Find its capacity in litres.

Q.

A box with lid is made of 2 cm thick wood. Its external length, breadth and height are 25 cm, 18 cm and 15 cm respectively. How much cubic cm of a liquid can be placed in it? Also, find the volume of the wood used in it.

Q.

Question 73

A hedge boundary needs to be planted around a rectangular lawn of size $72m\times 18$ m. If 3 shrubs can be planted in a metre of hedge, how many shrubs will be planted in all?

Q. What is the volume of a right circular cone of base radius r, height h and slant height l?

1. $\pi r^{2}h$
2. $\frac{1}{2}\pi r^{2}h$
3. $\frac{1}{3}\pi r^{2}h$
4. $2\pi r^{2}h$

Q.

If the object is solid, the space occupied by such an object is called volume and if the object is hollow, the space that can be filled is called ___

Q. A hemispherical tank of radius 3 cm is full of milk. It is connected to a pipe, through which liquid is emptied at the $\frac{1}{7}$ litre per second. The time taken to empty the tank completely?

1. 0.302 sec
2. 0.396 sec
3. 0.453 sec
4. 0.492 sec

Q.

Find the volume of a cone with a diameter of $10yards$ and a height of $12yards$. Round your answer to the nearest tenth.

Q. The number of cubes of side 2 cm that can be placed inside a box of dimensions 10 x 4 x 2 cm is

1. 10
2. 5
3. 15

Q.

A solid cylinder is melted and cast into a cone of same radius.The heights of the cone and cylinder are in the ratio

1. 1:3

2. 9:1

3. 1:9

4. 3:1

Q.

The area of cross section of a pipe is 10 sq. cm and the speed of water flowing throught it is 20 cm/s. How long will it take to fill a tank whose capacity is 240 litres?

1. 15 minutes.

2. 18 minutes.

3. 22 minutes.

4. 20 minutes.

Q.

Water flow in a tank 150 m x 100 m at the base, through a pipe whose cross section is 0.2 m by 0.15 m at the speed of 15 km/hour. In what time, will the water be 3 metres deep?

1. 100 hrs.

2. 10 hrs.

3. 50 hrs.

4. 80 hrs.

Q.

A solid cylinder of height 4m is melted and recasted into a cone retaining the radius.The height of the cone is

1. 12m

2. 4m

3. 24m

4. 16m

Q. A semi-circular sheet of metal of diameter 56 cm is bent to form an open conical cup. The approximate capacity of the cup is

1. $\frac{2744\sqrt{3}\pi }{3}c{m}^3$
   
2. $1523\pi c{m}^3$
3. $\frac{1372\sqrt{3}\pi }{3}c{m}^3$
   
4. $\frac{1946\sqrt{3}\pi }{3}c{m}^3$
   

Q. A semi-circular sheet of metal of diameter 28cm and is bent into an open conical cup. Find depth and capacity of cup.

1. 
   663.346 cm${}^3$
2. 
   435.098 cm${}^3$
3. 
   622.365 cm${}^3$
4. 
   755.456 cm${}^3$

Q. A pyramid has a square base with a slant height of $17cm$ and a vertical height of $15cm$. What is the volume of the pyramid?​

Q.

Four circular windows, each of radius $28cm$ are to be fitted with glass. Calculate the cost of glass at the rate of $Rs.4.25$ per $m^2.$

1. $Rs.4.20$

2. $Rs.8.20$

3. $Rs.9.20$

4. $Rs.3.8$

Q.

State if the following statements are True or False. Correct the false statement.
Equal volumes of different liquids have equal masses.

1. True
2. False

Q.

Question 1
If the radius of a sphere is 2r, then its volume will be:

A) $\frac{4}{3}\pi r^3$
B) $4\pi r^3$
C) $\frac{8}{3}\pi r^3$​​​​​​​
D) $\frac{32}{3}\pi r^3$​​​​​​​

Q.

A cylindrical bucket of height 18cm, had $1200c{m}^3$ of water.

This water was used to fill a cuboid having base dimensions 8cm x 10cm. After filling the cuboid, 6 cm of water still remained in the cylindrical bucket, find the height of the cuboidal box.

1. $12cm$

2. $9cm$

3. $10cm$

4. $8cm$

Q.

The dimensions of a car pertol tank is 50cm x 32cm x 24 cm. If is full of petrol. The cars petrol consumption is 15km per litre. Find the maximum distance that can be covered by the car.

1. 550 km.

2. 576 km.

3. 570 km.

4. 566 km.

Q.

How many cubic centimetres of iron are there in an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm, the iron being 1.5 cm thick throughout? If 1 cubic cm of iron weighs 15 g, find the weight of the empty box in kg.

Q.

A tank’s capacity is 1600 $c{m}^3$. If the time taken by tap to empty the tank is 20 min, then the rate of emptying the tank is __ $c{m}^3/min$

Q.

Determine the ratio of the length of the longest rod that can be fitted in a sphere to the length of the longest rod that can be fitted in a cube, given that the sphere exactly fits inside the cube.

1. $\sqrt{3}:1$

2. $1:\sqrt{3}$

3. 1 : 1

4. 2 : 1

Q.

The given figure is net of a ______and the circumference of a circle is_____.

Q.

A hemispherical bowl is made of steel $0.25cm$ thick. The inside radius of the bowl is $5cm$. Find the volume of steel used in making the bowl.

Q. If 4 families each use 4 buckets of 16 m${}^3$ water daily from a 4096 m${}^3$ tank, then the water will last for .

1. 16 days
2. 21 days
3. 14 days

Q.

Four cubes each of side 5 cm are joined end to end. The volume of the resulting cuboid is

1. 400 cm³

2. 300 cm³

3. 600 cm³

4. 500 cm³

Q. The ratio of the curved surface areas of two cylinders is 1 : 3. If the ratio of the heights of the two cylinders is 2 : 3, then the ratio of their volumes is

1. 1 : 2
2. 1 : 3
3. 1 : 6
4. 2 : 9

Q. A solid cube of side length $k$ is dropped into a cubical vessel partly filled with water. The length of side of the vessel is 200% more than the length of the solid cube. If the solid cube is completely submerged, then the increase in water level in the vessel is

1. $\frac{k}{27}$
   
2. $\frac{k}{9}$
   
3. $\frac{k}{3}$
   
4. 3$k$

Q.

The volume of a cuboid is x³ – x² – 2x cubic units. If x=5 what are the dimensions?

1. 6, 7, 8

2. 3, 7, 5

3. 5, 3, 6

4. 2, 5, 6