# NCERT Solutions for Class 9th Mathematics

## Chapter 13. Surface Areas and Volumes

### Exercise 13.6

**EXERCISE 13.6**

**Assume π** **= 22/7****, unless stated otherwise.**

**Q1. 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 cm ^{3} = 1 l)**

**Solution:**

Circumference of cylinder = 132 cm

Height = 25 cm

2πr = 132 cm

**Q2. 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.**

**Solution:**

Inner radius = 24 cm

Outer radius = 28 cm

(i) volume of inner cylinder = πr^{2}h

⇒ 110 × 196

⇒ 21560 cm^{3}

Total volume = v_{1} + v_{2}

⇒ 15840 + 21560 cm^{3}

⇒ 37400 cm^{3}

Mass = 37400 × 0.6

⇒ 22440

**Q3. 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:**

Length = 5cm, breadth = 4cm, height = 15cm

Diameter = 7cm, height = 10cm, r = 3.5cm

Volume of cuboid = l × b × h

⇒ 5 × 4 × 15 cm

⇒ 20 × 15 cm

⇒ 300 cm^{3}

Volume of cylinder = πr^{2}h

⇒ × 3.5 × 3.5 × 10

⇒ 22 × 5 × 3.5

⇒ 110 × 3.5

⇒ 385 cm^{3}

Capacity of both

300 cm^{3 }= 385 cm^{3}

⇒ 385 – 300

⇒ 85 cm^{3}

**Q4. 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 ** **= 3.14)**

**Solution:**

Height = 5 cm

Lateral surface area of the cylinder = 2πrh

2 × 3.14 × r × 5 = 94.2 cm^{2}

**Q5. 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:**

Cost = Rs. 2200

Height = 10 m

**Q6. 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? **

**Solution:**

Height = 1 m

Capacity = 15.4 l

**Q7. 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:**

**Q8. 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:**