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

Question - 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.

Answer - 21 : -

Let radius of cylinder = r
and radius of cone = r
and let height of cylinder = h
and height of cone = h

Question - 22 : - A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground. Find the area of the canvas required for the tent.

Answer - 22 : -

Diameter of the cylindrical portion = 24 m 24
∴ Radius (r) = 24/2 = 12 m
Height of cylindrical portion = 11 m
and total height = 16 m
 
∴ Height of conical portion = 16 – 11 = 5 m
∴ Slant height of the conical portion (l)

Question - 23 : - A circus tent is cylindrical to a height of 3 meters and conical above it. If its diameter is 105 m and the slant height of the conical portion is 53 m, calculate the length of the canvas 5 m wide to make the required tent.

Answer - 23 : - Diameter of the cylindrical tent = 105 m

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