# NCERT Solutions for Class 9th Mathematics

## Chapter 13. Surface Areas and Volumes

### Exercise 13.7

**EXERCISE 13.7**

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

**1. Find the volume of the right circular cone with**

**(i) radius 6 cm, height 7 cm (ii) radius 3.5 cm, height 12 cm**

**Solution:**

**2. Find the capacity in litres of a conical vessel with**

**(i) radius 7 cm, slant height 25 cm (ii) height 12 cm, slant height 13 cm**

**Solution:**

(i) h^{2} = 25^{2} - 7^{2}

**3. The height of a cone is 15 cm. If its volume is 1570 cm ^{3}, find the radius of the base.(Use π**

**= 3.14)**

**Solution:**

Height = 15 cm, volume = 1570 cm^{3}

^{}

**4. If the volume of a right circular cone of height 9 cm is 48π** **cm ^{3}, find the diameter of its base.**

**Solution:**

Height = 9 cm, volume = 48π cm^{3}

^{}

**5. A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?**

**Solution:**

Diameter = 3.5 cm , height = 12 cm , radius = 1.75

**6. The volume of a right circular cone is 9856 cm3. If the diameter of the base is 28 cm, find**

**(i) height of the cone (ii) slant height of the cone**

**(iii) curved surface area of the cone**

**Solution:**

Volume = 9856 cm^{3} , diameter = 28 cm , radius = 14cm

**7. A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.**

**Solution:**

Height = 12 cm , radius = 5 cm

**8. If the triangle ABC in the Question 7 above is revolved about the side 5 cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained in Questions 7 and 8.**

**Solution:**

Height = 5 m , radius = 12 m

**9. A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.**

**Solution:**

Diameter = 10.5 m, height = 3 m , radius = 5.25