# Surface Areas and Volumes – Exercise 13.3 – (MATHEMATICS) – 9th Class

**Exercise 13.3 **

Assume 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.**

### Show Answer

**Sol.** Curved surface area =

= 165 cm²

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

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**Sol.** Total surface area = πrl + πr² = πr(l + r)

= 1244.57 m^{2}

**3. Curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find**

**(i) radius of the base and**

**(ii) total surface area of the cone.**

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**Sol.** (i) Given: πrl =

∴ Radius of the base = 7 cm.

(ii) Total surface area = πrl + πr²

**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 m² canvas is Rs.70.**

### Show Answer

**Sol.** Base radius = 24 m, height = 10 m.

(i) Slant height =

(ii) Total canvas required = 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 n = 3.14).**

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**Sol.** Slant height aof the tent = = 10 m.

Area of tarpailin required = πrl = 3.14 × 6 × 10 m²

= 188.4 m².

∴ Length of tarpaulin required = = 62.8 m.

Total length required including wastage = (62.8 + 0.2) m = 63 m.

**6. The slant height and base diameter of a conical tomb are 25 in and 14 m respectively. Find the cost of whitewashing its curved surface at the rate of t210 per 100 m ^{2}.**

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**Sol.** Curved surface area = πrl =

Cost of white-washing = Rs.

**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.**

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**Sol.** Slant height of joker’s cap

∴ Area of sheet required for 10 caps

**8. A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each one 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 Rs.12 per m², what will be the cost of painting all these cones? (Use π = 3.14 and take = 1.02.)**

### Show Answer

**Sol.** Slant height of each cone (*l*) =

=

∴ Area to be painted for 50 hollow cones

= 50 × πrl

= (50 × 3.14 × 0.2 × 1.02) m²

= 32.028 m²

Cost of painting = Rs.(12 × 32.028)

= Rs. 384.34 (approx).