Question

In order to provide shelter to flood victims, a shed was constructed using tin sheets, which is in the form of a cuboid surmounted by a half cylinder as shown below:

The length, breadth and height of the cuboidal portion are 10 m, 7 m and 3 m, respectively. The diameter of the cylindrical portion is 7 m. Find the cost of tin sheets required to make the shed at the rate of ₹ 70 per square metre, given that the shed is open from the front side and closed from the back side.

Answer 1

Length of cuboid (l) = 10 m

Breadth of cuboid (b) = 7 m

Height of cuboid (h) = 3 m

Radius of cylinder (r) = `7/2` m

Curved surface area of a half cylinder = `1/2 (2πrH)`

= πrH

= `22/7 xx 7/2 xx 10`

= 110 sq. m

Area of the back portion = l × b

= 70 × 7

= 70 m²

Area of two sides = 2(b × h)

= 2 × 7 × 3

= 42 m²

Area of top (excluding cylindrical portion) = l × h

= 10 × 3

= 30 m²

∴ Surface area of cuboid = 70 + 42 + 30

= 142 m²

Total area = Surface area of cuboid + Curved surface area of a half cylinder

= 142 + 110

= 252 m²

Total cost = 252 × 70

= ₹ 17640