Relation between Volume and Capacity

Q.

The diameters of the Sun and earth are 1.4 × 10⁹ meters and 1.275 × 10⁷ respectively. Compare them

Q.

1 micron equals to :

a) 1/10000 m. b) 10⁶ dm.

c) 10^-6 m. d) 10^-4cm.

Q.

If the capacity of a cylindrical tank is $1848m^3$ and the diameter of its base is 14 m, the depth of the tank is

(a) 8 m

(b) 12 m

(c) 16 m

(d) 18 m

Q.

Calculate the volume of a cylinder of radius 5 cm and height 10 cm.

Q. The diameter of a wheel of a bus is 90 cm which makes 315 revolutions per minute. Determine it's speed in kilometers per hour.(Use π=22/7)

Q. Question 8
Water is pouring into a cuboidal reservoir at the rate of 60 litres per minute. If the volume of reservoir is $108m^3$ find the number of hours it will take to fill the reservoir.

Q.

Two cylinders A and B are formed by folding a rectangular sheet of dimensions $20cm\times 10cm$ along its length and also along its breadth respectively. Then, volume of A is ___ of volume of B.

Q. Which of the following is true about capacity?

1. It refers to the amount of space occupied by an object.
2. It refers to the quantity that a container holds.
3. It is measured in $c{m}^2$
4. It is the same as volume.

Q. The three dimensional space occupied by a solid is called its ___________.

1. Volume
2. Capacity
3. Area
4. Surface area

Q.

A milk container is 8 cm long and 50 cm wide. What should be its height so tha hold 4 litres of milk?

Q.

A closed box measures 66 cm, 36 cm and 21 cm from outside. If its walls are made of metal-sheet, 0.5 cm thick; find:

i) The capacity of the box;

ii) Volume of metal - sheet and

iii) Weight of the box, if $1c{m}^3$ of metal weights 3.6 gm.

Q. The amount of space inside a container that can be filled with either a solid, liquid or gas is called ____________.

1. Area
2. Total surface area
3. Capacity
4. Volume

Q.

Volume of liquid is usually expressed in _____

Q. Which of the following is true about volume?

1. It is measured in $c{m}^2$.
2. It is measured in litres (L).
3. Volume refers to the amount of space occupied by an object.
4. It is the same as capacity.

Q. Find the volume of a cylinder, the diameter of whose base is 7cm and height being 60cm. Also, find the capacity of the cylinderin litres.

Q.

Question 5

If the height of a cylinder becomes $\frac{1}{4}$ of the original height and the radius is doubled, then which of the following will be true ?
(a) Volume of the cylinder will be doubled
(b) Volume of the cylinder will remain unchanged
(c) Volume of the cylinder will be halved
(d) Volume of the cylinder will be $\frac{1}{4}$ of the original volume

Q.

Water is being poured into a cuboidal reservoir at the rate of 60 litres per minute. If the sides of the reservoir are 9m, 6m and 2m, find the number of hours it will take to fill the reservoir. [4 MARKS]

Q. Question 6
A milk tank is in the form of a cylinder whose radius is 1.5 m and length is 7 m. Find the Quantity of milk in liters that can be stored in the tank.

Q.

The inner volume of a container is called its capacity

1. True
2. False

Q. Question 8
Water is pouring into a cuboidal reservoir at the rate of 60 litres per minute. If the volume of reservoir is $108m^3$ find the number of hours it will take to fill the reservoir.

Q.

Question 34

The volume of a cylinder becomes ___ the original volume if its radius becomes half of the original radius.

Q.

Formula to find the volume of cylinder is:

1. 

2. 

3. 

4. 

Q.

Cod Fish World maintains a storage tank for sea water.

The tank has a volume of $20000000$gallons and is supplied from the ocean by a pipe which pumps $80000$ gallons per hour.

Water is pumped back to the ocean at the same rate.

An aquarium holding $300000$ gallons is fed from the storage tank through a pipe which carries $6000$ gallons per hour, and water is pumped back into the storage tank at the same rate.

Ocean water contains approximately $0.14$ kilograms of salt per gallon.

If $Qs$ is the amount of salt in the storage tank and $QA$ is the amount in the aquarium, measured in kilograms, and time is measured in hours, they obey the equations:

1. $$\begin{gathered} Q_S=\frac{Q_A}{50}-\frac{43Q_S}{10000}+11200 \\ {Q}_A=840-\frac{Q_A}{50} \end{gathered}$$

2. $$\begin{gathered} Q_S=\frac{Q_A}{50}-\frac{Q_S}{250}+11200 \\ {Q}_A=\frac{3Q_S}{10000}-\frac{Q_A}{50} \end{gathered}$$

3. $$\begin{gathered} Q_S=\frac{Q_A}{50}-\frac{43Q_S}{10000}+0.14 \\ {Q}_A=\frac{3Q_S}{10000}-\frac{Q_A}{50} \end{gathered}$$

4. $Q_S=\frac{Q_A}{50}-\frac{43Q_S}{10000}+11200$

Q.

The capacity of a soda can be calculated using the formula.

1. 2πr(r+h)

2. 2πr

3. π$r^2$h

4. All of these

Q. Water is poured into a cuboidal reservoir at the rate of 60 litres per minute. If the volume of reservoir is $108m^3$. Find the number of hours it will take to fill the reservoir.

Q.

Volume can be expressed as

1. cubic centimeter

2. cubic meter

3. millimeter

4. all of the above

Q. A water tank is 1.4 m long, 1m wide and 0.7m deep. Find the volume of the tank in litres.

Q.

What is volume? What is its SI unit?

Q.

Question 90

The radius and height of a cylinder are in the ratio 3 : 2 and its volume is $19404c{m}^3$. Find its radius and height.

Q.

1. 60 cm²

2. 50 cm²

3. 80 cm²

4. 40 cm²