### Question 1. The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many liters of water can it hold? (1000 cm^{3} = 1l)

**Solution:**

Given values,

Circumference of the base of a cylindrical = 132 cm

Height of cylinder (h)= 25 cm

Base of cylinder is of circle shape, having

circumference = 2πr(r is radius)Hence, 2πr = 132 cm

r = 132/(2 × (22/7)) (taking π=22/7)

r = (132 × 7)/(2 × 22)

r = 21 cmSo,

volume of cylinder = πr^{2}h= 22/7 × 21 × 21 × 25 (taking π=22/7)

= 34650 cm^{3}

As, 1000 cm

^{3}= 1 litre34650 cm

^{3}= (1/1000) × 34650= 34650/1000

= 34.650 litres

### Question 2. The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm^{3} of wood has a mass of 0.6 g.

**Solution:**

Given values,

Inner radius of cylinder (r

_{1})= 24/2 = 12 cmOuter radius of cylinder (r

_{2})= 28/2 = 14 cmHeight of cylinder (h)= 35 cm

So,

volume used to make wood = volume of outer cylinder – volume of outer cylinder

= π(r_{2}^{2})h – π(r_{1}^{2})h= π(r

_{2}^{2}– r_{1}^{2})h= 22/7 × (14

^{2}– 12^{2}) × 35 (taking π=22/7)= 22/7 × (52) × 35

= 5720 cm^{3}As, 1 cm

^{3}= 0.6 g5720 cm

^{3 }= 0.6 × 5720 g

= 3432 grams

= 3.432 kg

### Question 3. A soft drink is available in two packs –

### (i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and

### (ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm.

### Which container has greater capacity and by how much?

**Solution:**

Let’s see each case,

(i)The shape of can is cuboid here, as having rectangular baseGiven values,

Length of can (l) = 5 cm

Width of can (b) = 4 cm

Height of can (h) = 15 cm

So,

The amount of soft drink it can hold= volume of cuboid=

(l × b × h)= 5 × 4 × 15 cm

^{3}

= 300 cm^{3}

(ii)The shape of can is cylinder here, as having circular baseGiven values,

Radius of can (r) = 7/2 cm

Height of can (h) = 10 cm

So,

The amount of soft drink it can hold= volume of Cylinder

= (πr^{2}h)= 22/7 × 7/2 × 7/2 × 10 cm

^{3 }(taking π=22/7)

= 385 cm^{3}

Hence, we can see the can having circular base can contain (385 – 300 = 85 cm^{3}) more amount of soft drinks than first can.

### Question 4. If the lateral surface of a cylinder is 94.2 cm^{2} and its height is 5 cm, then find

**(i) radius of its base **

**(ii) its volume. (Use π = 3.14)**

**Solution:**

Given values,

Lateral surface of cylinder = 94.2 cm

^{2}Height of cylinder (h) = 5 cm

Let’s see each case,

(i)So, the lateral surface is of rectangle shape whose

length = (circumference of base circle of cylinder)andwidth = height of cylinderLet the base radius = r

Lateral surface = length × width94.2 cm

^{2 }= (2πr) × h (circumference of circle = 2πr)94.2 cm

^{2 }= (2 × 3.14 × r) × 5 (taking π=3.14)r = 94.2 / (2 × 3.14 × 5)

r = 3 cm

(ii)Given values,Radius of cylinder (r)= 3 cm

So,

the volume of cylinder = (πr^{2}h)= π × 3 × 3 × 5 cm

^{3}= 3.14 × 3 × 3 × 5 cm

^{3}(taking π=3.14)

= 141.3 cm^{3}

### Question 5. It costs ₹2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of ₹20 per m^{2}, find

**(i) Inner curved surface area of the vessel,**

**(ii) Radius of the base,**

**(iii) Capacity of the vessel**

**Solution:**

Given values,

Height of cylinder (h) = 10 m

Cost of painting rate = ₹20 per m

^{2}Let’s see each case,

(i)For 1 m^{2 }= ₹20For lateral surface = ₹2200

So the lateral surface = 2200 / 20

= 110 m^{2}

(ii)Let the base radius = r

So as, Lateral surface = (circumference of base circle of cylinder) × height

110 m^{2}= (2πr) × h110 = (2 × 22/7 × r) × 10 (taking π=22/7)

r = 110 × 7 / (2 × 22 × 10) cm

r = 7/4 cm

r = 1.75 cm

(iii) Volume of cylinder = (πr^{2}h)= 22/7 × 7/4 × 7/4 × 10 cm

^{3 }(taking π=22/7)

= 96.25 cm^{3}

### Question 6. The capacity of a closed cylindrical vessel of height 1 m is 15.4 liters. How many square meters of metal sheet would be needed to make it?

**Solution:**

Given values,

Height of cylinder (h) = 1 m = 100 cm

Volume of cylinder (V)= 15.4 liters

As

1 liter = 1000 cm^{3}15.4 liters = 15.4 × 1000 cm

^{3}V = 15,400 cm

^{3}

Volume of cylinder = (πr^{2}h)15,400 = 22/7 × r

^{2}× 100 (taking π=22/7)r

^{2}= 15,400 × 7 /(22 × 100)r

^{2}= 49r = √49

r = 7 cm

Surface area of a closed cylinder =(curve surface area + top and bottom circle) = 2πrh + (2 × πr^{2})= 2πr (r+h)

= 2 × 22/7 × 7 × (7 + 100) cm

^{2 }(taking π=22/7)= 2 × 22 × 107

= 4708 cm

^{2}

= 0.4708 m^{2}

Hence, 0.4708 m^{2 }of metal sheet would be needed to make it.

### Question 7. A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.

**Solution:**

So here

pencil = (cylinder of wood + cylinder of graphite)Given values,

Height of wood (and graphite) cylinder (h) = 14 cm = 140 mm

Radius of pencil (R)= 7/2 mm

Radius of graphite (r)= 1/2 mm

Volume of Graphite = (πr^{2}h)= 22/7 × 1/2 × 1/2 × 140 mm

^{3 }(taking π=22/7)

= 110 mm^{3}

= 0.11 cm^{3}

Volume of wood = Volume of pencil – Volume of graphite

=(πR^{2}h) – (πr^{2}h) =π(R^{2}– r^{2})h= 22/7 × ((7/2)

^{2}– (1/2)^{2}) × 140 mm^{3 }(taking π=22/7)= 22 × 20 × ((49/4) – (1/4)) mm

^{3}= 22 × 20 × 12 mm

^{3}

= 5280 mm^{3}

= 52.80cm^{3}

### Question 8. A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?

**Solution:**

So here

Volume of soup for each patient = Volume of cylinder.Given values,

Height of cylinder (h) = 4 cm

Radius of cylinder (r)= 7/2 cm

Volume of Cylinder = (πr^{2}h)= 22/7 × 7/2 × 7/2 × 4 cm

^{3 }(taking π=22/7)= 154 cm

^{3 }Volume of soup for 250 patient = 250 × Volume of cylinder.

= 250 × 154

= 38,500 cm^{3}

Hence, 38,500cm^{3 }soup is needed daily to serve 250 patients.