Class IX Math NCERT Solution for Surface Areas and Volumes 13.3

EXERCISE 13.3 (Page 221)
Q1.   Diameter of the be of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.
Sol: Here, diameter of the base = 10.5 cm
           
Q2.   Find the total surfce area of a cone, if its slant height is 21 m and diameter of its base is 24 m.
Q3.   Curved surface area of a cone is 308 cm' and its slant height is 14 cm. Find: (i) radius of the base and (ii) total surface area of the cone.
Sol: Here, curved surface area = 308 cm2 Slant height (1) = 14 cm
                 (i) Let the radius of the base be 'r' cm.
                 ∴ πrl = 308
                 
                 and curved surface area = 308 cm2
                 ∴ Total surface area = [Curved surface area] + [Base area]
                 = 308 cm2 + 154 cm2
                 = 462 cm2
Q4.   A conical tent is 10 m high and the radius of its base
           (i) slppnt height of the tent.
           (ii) cost, of the canvas required to make the tent, if the cost of 1 m2 canvas is Rs. 70.
Sol: Here, height of the tent (h) = 10 m
           Radius of the base (r) = 24 m
           
Q5.   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).
Sol: Here, Base radius (r) = 6 m
           Height (h) = 8 m
           
           ∴ Area of the canvas (tarpaulin) required to make the tent = 188.4 m2
           Let the length of the tarpaulin = 'L' m
           ∴ Length × Breadth = 188.4
           ⇒ L × 3 = 188.4
           
Q6.   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 Rs. 210 per 100 m2.
Q7.   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.
Sol: Here,
           Radius of the base (r) = 7 cm
           height (h) = 24 cm
           
           Lateral surface area of 10 caps = 10 × 550 cm2 = 5500 cm2
           Thus, the required area of the sheet = 5500 cm2
Q8.   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 f 12 per m2, what will be the cost of painting ail the cones? (Use π = 3.14 and take 
Sol: Here,
           ∵ Diameter of the base = 40 cm
           
           

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