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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 Rs. 12 per , what will be the cost of painting all these cones? (Use π = 3.14 and take 1.04 = 1.02)
Diameter is 40 Cm first will get the radius in metre
40/100 =0.4
0.4/2= 0.2 (since the radius is always half of the diameter) therefore radius is 0.2m
H=1mTherefore use formula for surface area
πrl= 3.14x0.2x1.02 =0.640 meter square this is for one cone
For 50 cones =
50x 0.640 =32.0 metre square
Cost of painting for meter square area is 12 rs, so the cost for the 32.02-metre square area will be following
12 x 32.02 = 384.34 Rs
Hence it will cost 384.34 rs for 50 cones painting
Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.
Radius (r) of the base of cone =
= 5.25 cm
Slant height (l) of cone = 10 cm
CSA of cone = πrl
Therefore, the curved surface area of the cone is 165 cm2.
Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.
Radius (r) of the base of cone =
= 12 m
Slant height (l) of cone = 21 m
Total surface area of cone = πr(r + l)
Curved surface area of a cone is 308 and its slant height is 14 cm. Find (i) radius of the base and (ii) total surface area of the cone.
(i) Slant height (l) of cone = 14 cm
Let the radius of the circular end of the cone be r.
We know, CSA of cone = πrl
Therefore, the radius of the circular end of the cone is 7 cm.
(ii) Total surface area of cone = CSA of cone + Area of base
= πrl + πr2
Therefore, the total surface area of the cone is 462 cm2.
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 canvas is Rs. 70.
(i) Let ABC be a conical tent.
Height (h) of conical tent = 10 m
Radius (r) of conical tent = 24 m
Let the slant height of the tent be l.
In ΔABO,
AB2 = AO2 + BO2
l2 = h2 + r2
= (10 m)2 + (24 m)2
= 676 m2
∴ l = 26 m
Therefore, the slant height of the tent is 26 m.
(ii) CSA of tent = πrl
Cost of 1 m2 canvas = Rs 70
Cost of 
canvas =
= Rs 137280
Therefore, the cost of the canvas required to make such a tent is
Rs 137280.
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 = 3.14).
Height (h) of conical tent = 8 m
Radius (r) of base of tent = 6 m
Slant height (l) of tent =
CSA of conical tent = πrl
= (3.14 × 6 × 10) m2
= 188.4 m2
Let the length of tarpaulin sheet required be l.
As 20 cm will be wasted, therefore, the effective length will be (l − 0.2 m).
Breadth of tarpaulin = 3 m
Area of sheet = CSA of tent
[(l − 0.2 m) × 3] m = 188.4 m2
l − 0.2 m = 62.8 m
l = 63 m
Therefore, the length of the required tarpaulin sheet will be 63 m.
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 .
Slant height (l) of conical tomb = 25 m
Base radius (r) of tomb = 
7 m
CSA of conical tomb = πrl
= 550 m2
Cost of white-washing 100 m2 area = Rs 210
Cost of white-washing 550 m2 area =
= Rs 1155
Therefore, it will cost Rs 1155 while white-washing such a conical tomb
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.#new_questieon#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
Rs. 12 per , what will be the cost of painting all these cones? (Use
= 3.14 and take
)
Radius (r) of conical cap = 7 cm
Height (h) of conical cap = 24 cm
Slant height (l) of conical cap =
CSA of 1 conical cap = πrl
CSA of 10 such conical caps = (10 × 550) cm2 = 5500 cm2
Therefore, 5500 cm2 sheet will be required.
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