Q) 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.

(Q 27 A – 30/4/2 – CBSE 2026 Question Paper)

Ans:

Step 1: Given dimensions of the Cuboid:

Length, l = 25 m, Width, w = 14 m, Height, h = 16 m.

Step 2: Given dimensions of Semi-cylinder:

The height of the cylinder, h = length of the cuboid, l = 25 m

The diameter of the semi-cylinder d = width of the cuboid w = 14 m

So, the radius of the semi-cylinder r = = 7 m.

Step 3: Total Surface Area of 4 walls of cuboid

= 2 lh + 2 wh = 2 h (l + w)

= 2 (16)( 25 + 14) = 2 x 16 x 39 = 1248 m ²

Step 4: Total Surface Area of the Semi – Cylinder

= CSA of curved roof + Two semi circular ends

= π r l + 2 π r ²

= π r l + π r ² = π r (l + r) 

= (7)(25+7) = 22x 32 = 704 m ²

Step 5: Total Area of Cloth Required

= TSA of 4 walls of cuboid + TSA of the Semi – Cylinder

= 1248 + 704 = 1952 m ²

Therefore, total area of the cloth required is 1952 m ².

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