Shortcut Trick
Total paper area = Area of (Base + Back Face + 2 × Side Faces)
Required area = (80 × 30) + (80 × 40) + 2(30 × 40)
Required area = 2400 + 3200 + 2400 = 8000 cm2
Therefore, the area of the paper needed is 8000 cm2, which matches Option (2).
∴ The correct answer is 8000 cm2.
Alternate Method
Given:
⇒ Length (l) of the aquarium = 80 cm
⇒ Width (w) of the aquarium = 30 cm
⇒ Height (h) of the aquarium = 40 cm
Calculations:
⇒ Area of the Base = l × w = 80 × 30 = 2400 cm2
⇒ Area of the Back face = l × h = 80 × 40 = 3200 cm2
⇒ Area of one side face = w × h = 30 × 40 = 1200 cm2
⇒ Area of two side faces = 2 × 1200 = 2400 cm2
⇒ Total area of paper needed = Area of Base + Area of Back face + Area of two side faces
⇒ Total Area = 2400 + 3200 + 2400 = 8000 cm2
This result corresponds to the value given in Option (2).
∴ The correct answer is 8000 cm2.
Additional Information
Total Surface Area of Cuboid
The total surface area (TSA) covers all six faces and is given by the formula 2(lw + wh + hl).
Lateral Surface Area (Area of 4 walls)
The area of the vertical faces (excluding top and base) is given by 2h(l + w).
Volume of a Cuboid
The amount of space inside the cuboid (capacity) is calculated as Volume = l × w × h.
Diagonal of a Cuboid
The longest rod that can be placed inside a cuboid is √(l2 + w2 + h2).