## EXERCISE 13.6

#### Page No 230:

#### Question 1:

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

#### Answer:

Let the radius of the cylindrical vessel be *r*.

Height (*h*) of vessel = 25 cm

Circumference of vessel = 132 cm

2π*r* = 132 cm

Volume of cylindrical vessel = π*r*^{2}*h*

= 34650 cm^{3}

= 34.65 litres

Therefore, such vessel can hold 34.65 litres of water.

#### 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.

#### Answer:

Inner radius (*r*_{1}) of cylindrical pipe =

Outer radius (*r*_{2}) of cylindrical pipe =

Height (*h*) of pipe = Length of pipe = 35 cm

Volume of pipe =

Mass of 1 cm^{3} wood = 0.6 g

Mass of 5720 cm^{3} wood = (5720 × 0.6) g

= 3432 g

= 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?

#### Answer:

The tin can will be cuboidal in shape while the plastic cylinder will be cylindrical in shape.

Length (*l*) of tin can = 5 cm

Breadth (*b*) of tin can = 4 cm

Height (*h*) of tin can = 15 cm

Capacity of tin can = *l × b* × *h*

= (5 × 4 × 15) cm^{3}

= 300 cm^{3}

Radius (*r*) of circular end of plastic cylinder =

Height (*H*) of plastic cylinder = 10 cm

Capacity of plastic cylinder = π*r*^{2}*H*

Therefore, plastic cylinder has the greater capacity.

Difference in capacity = (385 − 300) cm^{3 }= 85 cm^{3}

#### 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]

#### Answer:

(i) Height (*h*) of cylinder = 5 cm

Let radius of cylinder be *r*.

CSA of cylinder = 94.2 cm^{2}

2π*rh* = 94.2 cm^{2}

(2 × 3.14 × *r* × 5) cm = 94.2 cm^{2}

*r* = 3 cm

(ii) Volume of cylinder = π*r*^{2}*h*

= (3.14 × (3)^{2} × 5) cm^{3}

= 141.3 cm^{3}

#### Page No 231:

#### Question 5:

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

(i) Inner curved surface area of the vessel

(ii) Radius of the base

(iii) Capacity of the vessel

#### Answer:

(i) Rs 20 is the cost of painting 1 m^{2} area.

Rs 2200 is the cost of painting =

= 110 m^{2} area

Therefore, the inner surface area of the vessel is 110 m^{2}.

(ii) Let the radius of the base of the vessel be* r*.

Height (*h*) of vessel = 10 m

Surface area = 2π*rh* = 110 m^{2}

(iii) Volume of vessel = π*r*^{2}*h*

= 96.25 m^{3}

Therefore, the capacity of the vessel is 96.25 m^{3} or 96250 litres.

#### Question 6:

The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?

#### Answer:

Let the radius of the circular end be *r*.

Height (*h*) of cylindrical vessel = 1 m

Volume of cylindrical vessel = 15.4 litres = 0.0154 m^{3}

⇒ *r* = 0.07 m

Therefore, 0.4708 m^{2} of the metal sheet would be required to make the cylindrical vessel.

#### Question 7:

A lead pencil consists of a cylinder of wood with 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.

#### Answer:

Radius (*r*_{1}) of pencil == 0.35 cm

Radius (*r*_{2}) of graphite = = 0.05 cm

Height (*h*) of pencil = 14 cm

Volume of wood in pencil =

#### 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?

#### Answer:

Radius (*r*) of cylindrical bowl =

Height (*h*) of bowl, up to which bowl is filled with soup = 4 cm

Volume of soup in 1 bowl = π*r*^{2}*h*

= (11 × 3.5 × 4) cm^{3}

= 154 cm^{3}

Volume of soup given to 250 patients = (250 × 154) cm^{3}

= 38500 cm^{3}

= 38.5 litres.