# NCERT Solutions for Class 9th Mathematics

## Chapter 13. Surface Areas and Volumes

### Exercise 13.3

**EXERCISE 13.3**

**Assume that π** **= ** **, unless stated otherwise.**

**1. Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area. **

**Solution:**

Diameter = 10.5 cm Þ radius = 5.25, height = 10 cm

Curved surface area of cone = πrl

Þ × 5.25 × 10

Þ × 52.5

Þ 165 cm^{2}

**2. Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.**

**Solution:**

Slant height = 21 m , diameter = 24 m Þ radius = 12 m

Total surface area of cone = πr(l + r)

**3. Curved surface area of a cone is 308 cm ^{2} and its slant height is 14 cm. Find**

**(i) radius of the base and (ii) total surface area of the cone.**

**Solution:**

CSA of cone = 308 cm^{2}, height = 14 cm

(i) CSA of cone = 308 cm^{2}

**4. A conical tent is 10 m high and the radius of its base is 24 m. Find**

**(i) slant height of the tent.**

**(ii) cost of the canvas required to make the tent, if the cost of 1 m ^{2} canvas is 70. **

**Solution:**

Height = 10 cm, radius = 24 m

l^{2} = h^{2} + r^{2}

l^{2 }= 10^{2 }+ 24^{2}

l =

l = 26 m

(ii) curved surface area of cone = πrl

**5. What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm (Use π** **= 3.14).**

**Solution:**

Wide = 3 m , height = 8 , radius = 6 m

l^{2} = r^{2} + h^{2}

l^{2} = 6^{2 }+ 8^{2}

l =

l = 10 m

Curved surface area of cone = πrl

Þ 3.14 × 6 × 10

Þ 31.4 × 6

Þ 188.4 m^{2}

**6. The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of 210 per 100 m ^{2}.**

**Solution:**

Length = 25 m, diameter = 14 m, radius = 7 m

Curved surface area of cone = πrl

**7. A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.**

**Solution: **

Radius = 7 cm, height = 24 cm

l^{2} = r^{2} + h^{2}

l^{2} = 7^{2} + 24^{2}

**8. A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is 12 per m ^{2}, what will be the cost of painting all these cones? (Use π**

**= 3.14 )**

**Solution:**

Diameter = 40 cm, radius = 20 cm, height = 1 m

l^{2 }= r^{2} + h^{2}

l^{2} = 0.2^{2} + 1^{2}