#### Class Nine NCERT Sol Maths Surface Areas Volumes

## Chapter 13: Surface Areas and Volumes

#### TEXTBOOK’S EXERCISE – 13.7

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

**Sol.
**Here, r = 3 5
2. m = 1.75 m, h = 12
m

The capacity of the pit = 13 πr2h

= 13 × 22/7
× 1.75 × 1.75 × 12 m^{3}

= 38.5 m^{3} = 38.5 kl

**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) the slant height of the cone

(iii) the curved surface area of the cone.

**Sol. **Here, r = 28/2 cm
= 14 cm,

volume = 9856 cm^{3}

(i) Volume of the
cone = 1/3 πr^{2}h

⇒ 9856 = 1/3 × 22/7 × 14 × 14 × h

= 48

Hence, height of the cone = 48 cm

(ii) Slant height

Hence, slant height of the cone = 50 cm

(iii) Curved surface area of the cone

= πrl = 22/7 ×
14 × 50 cm^{2} = 2200 cm^{2}

**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. **

**Sol. **

The solid formed is a cone, whose height h = 12 cm, base radius

r = 5 cm.

∴ Volume of the cone = 13 πr^{2}h

= 1/3 × π ×
5 × 5 × 12 cm^{3} = 100 π cm^{3}

**8. If the triangle ABC in 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.**

**Sol.
**Here, radius *r *of the cone = 12 cm and height *h *of
the cone = 5 cm

∴ The volume of the cone = 1/3 π*r*^{2}*h*

= 1/3 π × 12 × 12 × 5 = 240 πcm^{3}

Hence, the required ratio

**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. **

**Sol. **Here, radius r = 10.5/ 2 m =
5.25 m, h = 3 m

Volume of the heap = 1/3 πr2h

= 1/3 × 22/7 × 5.25 × 5.25 × 3 m^{3} = 86.625 m^{3}

Curved surface area
of the cone = π*rl *

= 22/7 ×
5.25 × 6.05 m^{2} = 99.825 m^{2}

Hence, 99.825 m^{2} of canvas is needed.