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 \(14 \text{ m} \times 25 \text{ m} \times 16 \text{ m}\).

Hint:

Always visualize the surfaces covered. In shed problems, the floor is usually excluded. Also, ensure the radius and length of the semi-cylinder correctly correspond to the cuboid's dimensions from the diagram.

Answer 1

Step 1: Dimensions of Shed
Length (L) = 25 m
Width (W) = 14 m
Height (H) = 16 m

Radius of semi-cylinder:
r = W/2 = 14/2 = 7 m

Step 2: Area of Four Walls of Cuboid
Area of two longer walls:
= 2 × (L × H)
= 2 × (25 × 16)
= 800 m²

Area of two shorter walls:
= 2 × (W × H)
= 2 × (14 × 16)
= 448 m²

Total wall area:
= 800 + 448
= 1248 m²

Step 3: Curved Surface Area of Semi-cylinder
CSA = π r L
= (22/7) × 7 × 25
= 550 m²

Step 4: Area of Two Semi-circular Ends
Area = π r²
= (22/7) × 49
= 154 m²

Step 5: Total Cloth Required
Total area = 1248 + 550 + 154
= 1952 m²

Final Answer:
Total area of cloth required = 1952 m²