## Chapter 13 Surface Areas and Volumes Ex 13.6

**Question 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? (1000cm3 =1 L.)**
**Solution:**

We have, circumference of the base = 132 cm

∴ 2πr = 132

**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, inner diameter = 24 cm

Inner radius (r

_{1}) = 12cm

Outer diameter = 28 cm

Outer radius (r

_{2}) = 14cm

h = 35cm

**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.** **(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:**

**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:**

**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:**

We have, cost to paint the inner curved surface = ₹2200

Cost to paint per m

^{2}= ₹20

(i) Inner curved surface area of the vessel = 110m

^{2}

(ii) Hence, radius of the base is 1.75 m.

(iii) Capacity of the vessel = Volume of the vessel

**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?** **Solution:**

**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:**

**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:**