a tent of shape of a right circular cylinder upto a height of 3m and then becomes a right circular conewith height of 13.5m above the ground calculate the cost of painting the inner side of the text at the rate of RS 2 PER Sq m if radius of the base is 14m
Let r m be the radius of cylindrical base of cylinder of height h1 m.
∴ r = 14 m and h1 = 3 m
Curved surface area of cylinder = 2 πrh1 m2
The radius of cylindrical base of cylinder is also equal to the radius of right circular cone.
Let h2 be the height of cone and l be the slant height of cone.
r = 14 m and h2 = (13.5 - 3) m = 10.5 m
l2 = r2 + h22
l2 = (14)2 + (10.5)2
∴ Curved surface area of the cone = πrl
∴ Total area of tent which is to be painted
= Curved surface area of cylinder + Curved surface area of cone
= (264 + 770) m2
= 1034 m2
Now, Cost of painting 1 m2 of inner side of tent = Rs 2
∴ Cost of painting 1034 m2 inner side of tent = Rs 2 × 1034 = Rs 2068