Question - 11 : - A Joker’s cap is in the form of a right circular coneof base radius 7 cm and height 24 cm. Find the area of the sheet required tomake 10 such caps. [NCERT]

Answer - 11 : - Radius of the base of a conical cap (r) = 7 cm
and height (h) = 24 cm

Question - 12 : - Find the ratio of the curved surface areas of two cones if their diameters of the bases are equal and slant heights are in the ratio 4 : 3.

Answer - 12 : -

Let diameters of each cone = d

Then radius (r) =

Ratio in their slant heights = 4 : 3

Let slant height of first cone = 4x

and height of second cone = 3x

Now curved surface area of the first cone = 2πrh

Question - 13 : - There are two cones. The curved surface area of one is twice that of the other. The slant height of the later is twice that of the former. Find the ratio of their radii.

Answer - 13 : - In two cones, curved surface of the first cone = 2 xcurved surface of the second cone
Slant height of the second cone = 2 x slant height of first cone
Let r₁ and r₂ be the radii of thetwo cones
and let height of the first cone = h
Then height of second cone = 2h
∴ Curved surface of thefirst cone = 2πr₁h

Question - 14 : - The diameters of two cones are equal. If their slant heights are in the ratio 5 : 4, find the ratio of their curved surfaces.

Answer - 14 : -

Let diameter of one cone = d

and diameter of second cone = d

∴ Radius of the first cone (r) =

and of second cone (r2) =

Ratio in their slant heights = 5:4

Let slant height of the first cone = 5x

Then that of second cone = 4x

Now curved surface of the first cone = 2πrh

Question - 15 : - Curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find the radius of the base and total surface area of the cone. [NCERT]

Answer - 15 : - Area of curved surface of a cone = 308 cm²
and slant height (l) = 14 cm

Question - 16 : - 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. [NCERT]

Answer - 16 : - Slant height of a cone (l) = 25 m
and diameter of base = 14 m

Question - 17 : - A conical tent is 10 m high and the radius of its baseis 24 m. Find the slant height of the tent. If the cost of 1 m² canvas is Rs. 70, find the cost ofthe canvas required to make the tent. [NCERT]

Answer - 17 : -

Height of conical tent (A) = 10 m

Radius of the base (r) = 24 m

Question - 18 : - The circumference of the base of a 10 m height conical tent is 44 metres. Calculate the length of canvas used in making the tent if width of canvas is 2 m. (Use π = 22/7)

Answer - 18 : - Circumference of the base of a conical tent = 44 m

Question - 19 : - What length of tarpaulin 3 m wide will be required to make a conical tent of height 8 m and base radius 6 m? Assum that the extra length of material will be required for stitching margins and wastage in cutting is approximately 20 cm. (Use π = 3.14) [NCERT]

Answer - 19 : -

Height of the conical tent (h) = 8 m

and radius of the base (r) = 6 m

Now curved surface area of the tent = πrl = 3.14 x 6 x 10 = 188.4 m

Width of tarpaulin used = 3 m

∴ Length = 188.4 , 3 = 62.8 m

Extra length required = 20 cm = 0.2 m

∴ Total length of tarpaulin = 62.8 + 0.2 = 63 m

Question - 20 : - A bus stop is barricated from the remaining part of the road, by using 50 hollow cones made of recycled card-board. 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 these cones. (Use π = 3.14 and = 1.02) [NCERT]

Answer - 20 : -

Diameter of the base of tent = 40 cm

∴ Radius of the base of cone (r) = 40/2

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RD Chapter 20 Surface Areas and Volume of A Right Circular Cone Ex 20.1 Solutions

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