**Question 1. ****Given a cylindrical tank, in which situation will you find the surface area and in which situation volume**

**(a) To find how much it can hold.****(b) Number of cement bags required to plaster it.****(c) To find the number of smaller tanks that can be filled with water from it.**

**Solution:**

a) In this condition, we will find the

volumeof a cylindrical tank.b) In this condition, we will find the

surface areaof a cylindrical tank.c) In this condition, we will find the

volumeof a cylindrical tank.

**Question**** 2. ****The diameter of cylinder A is 7 cm, and the height is 14 cm. The diameter of cylinder B is 14 cm and the height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has a greater surface area?**

**Solution:**

Cylinder A:Radius of cylinder A = 7/2 cm

Height of cylinder A = 14 cm

Volume of cylinder A = pi.r

^{2}h = 22/7 x 7/2 x 7/2 x 14 = 539 cm^{3}Total Surface area of cylinder A = 2.pi.r(h + r) = 2 x 22/7 x 7/2(14 + 7/2) = 385 cm

^{2}

Cylinder B:

Radius of cylinder B = 14/2 or 7 cm

Height of cylinder B = 7 cm

Volume of cylinder B = pi.r

^{2}h = 22/7 x 7 x 7 x 7 = 1078 cm^{3}Total Surface area of cylinder B = 2.pi.r(h + r) = 2 x 22/7 x 7(7 + 7) = 616 cm

^{2}We can clearly see that the Volume of cylinder B is twice that of cylinder A.

Hence, verified thattheVolume of cylinder B is greater thanthevolume of cylinder A. Also, Total surface area of cylinder B is greater.

**Question 3. Find the height of a cuboid whose base area is 180 cm**^{2} and volume is 900 cm^{3}?

^{2}and volume is 900 cm

^{3}?

**Solution:**

Area of Cuboid = length x breadth = 180 cm

^{2}Volume of Cuboid = length x breadth x height = 900 cm

^{3}So, Area x height = Volume

180 cm

^{2 }x height = 900 cm^{3}Hence, height = 5 cm

Hence, height of given cuboid is 5 cm.

**Question 4. A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?**

**Solution:**

Volume of Cuboid = length x breadth x height = 60 cm x 54 cm x 30 cm = 97200 cm

^{3}Volume of Cube = (side)

^{3 }= (6cm)^{3}= 216 cm^{3}Number of small cubes that can be placed inside given cuboid = Volume of given Cuboid/ Volume of one Cube

= 97200/216

= 450

Hence, 450 small cubes can be placed inside given cuboid.

**Question 5. Find the height of the cylinder whose volume is 1.54 m**^{3} and diameter of the base is 140 cm?

^{3}and diameter of the base is 140 cm?

**Solution:**

Volume of cylinder = 1.54 m

^{3}Diameter of base of cylinder = 140 cm = 1.40 m, Radius = 7.20 m

As we know, Volume of cylinder = pi.r

^{2}hSo, 1.54 = 22/7 x 7.2 x 7.2 x height

On doing calculation, we get

Height of cylinder = 1 m

Hence, height of given cylinder is 1 m.

**Question 6. A milk tank is in the form of cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in litres that can be stored in the tank?**

**Solution:**

The radius of the cylindrical tank = 1.5 m

Length/Height of cylindrical = 7 m

The quantity of milk in liters that can be stored in the tank = Volume of the cylindrical tank

So, Volume of cylinder = pi.r

^{2}h = 22/7 x 1.5 x 1.5 x 7 = 49.50 m^{3}Volume = 49.50 m

^{3}As we know, 1 m

^{3}= 1000 litersSo, 49.50 m

^{3 }= 49500 L

Hence, thequantity of milk in liters that can be stored in the tank is49500 L

**Question 7. ****If each edge of a cube is doubled,**

**(i) how many times will it be surface area increase?****(ii) how many times will its volume increase?**

**Solution:**

Let us assume that the original edge of the cube is

acm. If the edge of the cube is doubled, then the new edge will be2acm.

i)Original surface area of cube = (edge)^{2 }= (a)^{2}= a^{2}cm^{2}New surface area of cube = (edge)

^{2 }= (2a)^{2}= 4a^{2}cm^{2}Ratio to find which cube’s surface area is greater = Original surface area : New surface area = a

^{2}: 4a^{2}= 1 : 4

Hence, surface area of cube is increased by 4 times.

ii)Original volume of cube = (edge)^{3 }= (a)^{3}= a^{3}cm^{3}New volume of cube = (edge)

^{3 }= (2a)^{3}= 8a^{3}cm^{3}Ratio to find which cube’s volume is greater = Original volume : New volume = a

^{3}: 8a^{3}= 1 : 8

Hence, volume of cube is increased by 8 times.

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

^{3}

**Solution:**

Given the volume of the reservoir is 108 m

^{3}Or 108000 L [1 m^{3}= 1000 L]. The volume of water pouring into a cuboidal reservoir = 60 L / minutes.So, the time is taken to fill the reservoir = Volume of cuboidal reservoir / Volume of water pouring into the reservoir per minute

= 108000/60

= 1800 minutes

= 1800/60

= 30 hours

Hence, it will require 30 hours to fill the reservoir completely.