Question 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: Here, diameter of the base = 10.5 cm
⇒ Radius (r) = (10.5/2)cm
Slant height (l) = 10 cm
∴ Curvered surface area of the cone = πrl
Question 2. Find the total surfce area of a cone, if its slant height is 21 m and diameter of its base is 24 m.
Solution: Here, diameter = 24 m
⇒ Radius (r) = (24/2)m = 12 m
Slant height (l) = 21 m
∴ Total surface area = πr(r + l)
Question 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.
Solution: Here, curved surface area = 308 cm2
Slant height (l) = 14 cm
(i) Let the radius of the base be ‘r’ cm.
Thus, the required radius of the cone is 7 cm.
and curved surface area = 308 cm2 [Given]
∴ Total surface area = [Curved surface area] + [Base area]
= 308 cm2 + 154 cm2 = 462 cm2
Question 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 70.
Solution: Here, height of the tent (h) = 10 m
Radius of the base (r) = 24 m (i)
∵ The slant height,
∴ The slant height of the tent =
Thus, the required slant height of the tent is 26 m.
(ii) ∵ Curved surface area of the cone = πrl
∴ Area of the canvas required =
Question 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 apπroximately 20 cm (Use π = 3.14).
Solution: 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 x Breadth = 188.4
⇒ L x 3 = 188.4
⇒ L= (188.4/3) = 62.8 m
Extra length of tarpaulin for margins = 20 cm = (20/100) m = 0.2 m
Thus, total length of tarpaulin required = 62.8 m + 0.2 m = 63.0 m
Question 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 m2.
Solution: Here, Base radius (r) = (14/7) = 7 m
Slant height (l) = 25 m
∴ Curved surface area = πrl = (22/7) x 7 x 25 m2
= 22 x 25 m2 = 550 m2
Cost of white washing:
Rate of whitewashing = 210 per 100 m2
∴ Cost of whitewashing for 550 m2
Question 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: Here, Radius of the base (r) = 7 cm height (h) = 24 cm
⇒ Lateral surface area of 10 caps = 10 x 550 cm2 = 5500 cm2
Thus, the required area of the sheet = 5500 cm2
Question 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 m2, what will be the cost of painting all these cones? (Use π = 3.14 and take √1.04= 1.02)
Solution: Here, ∵ Diameter of the base = 40 cm
∴ Radius (r) = 40/2 cm = 20 cm = 10/100 m
= 2/10 m = 0.2 m
Height (h) = 1 m
= 1.02 m [∵ √1.04= 1.02 (Given)]
Now, curved surface area = πrl
⇒ Curved surface area of 1 cone = 3.14 x 0.2 x 1.02 m2
⇒ Curved surface are of 50 cones
Cost of painting
∵ Rate of painting = ₹ 12 per m2
SURFACE AREA OF A SPHERE
A solid generated by revolving a circular lamina about any of its diameters, is called a sphere. If ‘r’ be its radius, then its surface area = 4πr2.
For the following πroblems, assume π = (22/7), unless stated otherwise.