Q23 of 63 Page 21

A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8 : 5, Show that the radius of each is to the height of each as 3 : 4.

For cylinder, we have


Base radius = r


Height = h


∴ Curved surface area S1 = 2πrh


For cone, we have


Slant height l =


S2 = πrl =πr


We have,


= =


==


(squaring both side )


= =


= 100h2 = 64r2+64h2


= 36h2 = 64r2


(Square root both side )


= 6h = 8r


==


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21

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

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A bus stop is barricaded from the remaining part of the road, by using 50 hollow cone 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 Rs. 12 per m2. What will be the cost of painting all these cones. (Use π=3.14 and = 1.02).

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Find the volume of a right circular cone with :

(i) radius 6 cm, height 7 cm.


(ii) radius 3.5 cm, height 12 cm


(iii) height 21 cm and slant height 28 cm.

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Find the capacity in litres of a conical vessel with :

(i) radius 7 cm, slant height 25 cm


(ii) height 12 cm, slant height 13 cm.