Question

To protect plants from heat, a shed of iron rods covered with green cloth is made. The lower part of the shed is a cuboid mounted by semi-cylinder as shown in the figure. Find the area of the cloth required to make this shed, if dimensions of the cuboid are 14 m × 25 m × 16 m.

Answer 1

Area of cloth = Lateral Surface Area of Cuboid + CSA of Semi-cylinder + Area of 2 Semicircles.

Dimensions: Length (L) = 25 m

Width (W) = 14 m

Height (H) = 16 m

For the semi-cylinder: Radius (r) = `W/2` = 7 m

Length (h_cyl) = 25 m

Lateral Surface Area of cuboid (4 walls):

LSA = 2(L + W) × H

= 2(25 + 14) × 16

= 2 × 39 × 16

= 1248 m²

Curved Surface Area of semi-cylinder:

CSA = `1/2 (2πrh_(cyl))`

= `πrh_(cyl)`

= `22/7 xx 7 xx 25`

= 550 m²

Area of 2 semi-circular ends:

Area_ends = `2 xx 1/2 πr^2`

= πr²

= `22/7 xx 7^2`

= 154 m²

Total Area = 1248 + 550 + 154

= 1952 m²

The total area of the cloth required is 1952 m².