Aquarium Paper Area Calculation

The problem asks for the total area to be covered with coloured paper on an aquarium shaped like a cuboid. The surfaces to be covered are the base, the two side faces, and the back face.

Given Dimensions:

The external measures of the cuboid aquarium are:

• Length ($l$) = $80 \text{ cm}$
• Width ($w$) = $30 \text{ cm}$
• Height ($h$) = $40 \text{ cm}$

Area Calculation Steps:

We need to calculate the area of each specified surface:

1. Base Area: The area of the base is calculated as length times width.

   Area_{base} = $l \times w$

   Area_{base} = $80 \text{ cm} \times 30 \text{ cm} = 2400 \text{ cm}^2$

2. Side Faces Area: There are two side faces, each with dimensions width times height. The total area of the two side faces is $2 \times (w \times h)$.

   Area_{sides} = $2 \times (w \times h)$

   Area_{sides} = $2 \times (30 \text{ cm} \times 40 \text{ cm}) = 2 \times 1200 \text{ cm}^2 = 2400 \text{ cm}^2$

3. Back Face Area: The area of the back face is calculated as length times height.

   Area_{back} = $l \times h$

   Area_{back} = $80 \text{ cm} \times 40 \text{ cm} = 3200 \text{ cm}^2$

Total Paper Needed:

The total area of paper needed is the sum of the areas calculated above.

Total Area = Area_{base} + Area_{sides} + Area_{back}

Total Area = $2400 \text{ cm}^2 + 2400 \text{ cm}^2 + 3200 \text{ cm}^2 = 8000 \text{ cm}^2$

Therefore, the area of the paper needed is $8000 \text{ cm}^2$.