# Surface Areas and Volumes – Exercise 13.6 – (MATHEMATICS) – 9th Class

**Exercise 13.6**

Assume π = , unless stated otherwise.

**1. The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold? (1000 cm³ = 1 l).**

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**Sol.** Circumference of base = 132 cm.

∴ Volume of cylindrical vessel = πr²h

∴ Capacity of the vessel = *l = 34.65 l*

Hence, vessel can hold 34.65 *l* of water.

**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 cm³ of wood has a mass of 0.6 g.**

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**Sol.** Volume of the wood = π(r_{1}^{2} – r_{2}^{2})h

= 110 (196 – 144) cm³ = 5720 cm³

Mass of the pipe (or wood) = 0.6 × 5720 g = 3432 g

= 3.432 kg.

**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?**

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**Sol.**

(i) Capacity of tin can = area of base × height

= (5 × 4) × 15 cm³ = 300 cm³

(ii) Capacity of the plastic cylinder

Hence, the plastic cylinder has greater capacity by 85 cm³.

**4. If the lateral surface of a cylinder is 94.2 cm² and its height is 5 cm, then find**

**(i) radius of its base**

**(ii) its volume. ** (Use π = 3.14)

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**Sol.** Given lateral surface = 94.2 cm².

(i) 2πrh = 94.2 ⇒ 2 × 3.14 × r × 5 = 94.2

⇒

(ii) Volume = πr²h = 3.14 × (3)² × 5 cm³ = 3.14 × 45 cm³ = 141.3 cm³.

**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 m², find**

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

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

**(iii) capacity of the vessel.**

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**Sol.** Cost of the painting is Rs.2200, if rate is Rs.20 per m²

(i) Inner curved surface area =

(ii)

(iii) Capacity of the vessel =

= 96.25 m³

**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?**

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**Sol.** Capacity of closed cylindrical vessel

= 15.4 *l*

= 15.4 × 1000 cm³ = 15400 cm³.

Height = 1 m = 100 cm.

∴

Area of metal sheet needed = 2πr(h + r)

= 4708 cm² = 0.4708 m².

**7. A lead pencil consists of a cylinder of mm wood with a solid cylinder of graphite filled in the interim: 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.**

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**Sol.** Volume of graphite

= 0.11 cm^{3}

Volume of wood = volume of cylinder – volume of graphite

= (5.39 – 0.11) cm^{3}

= 5.28 cm^{3}

**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?**

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**Sol.** Volume of soup for one patient =

Volume of soup for 250 patients = 250 × 154 cm³

= 38500 cm³ = 38.5 *l*.