Question: Find the total surface area of this cuboid. [Image description: A cuboid is shown with dimensions…

Find the total surface area of this cuboid.

[Image description: A cuboid is shown with dimensions labeled as follows: length = 7.5 cm, width = 2.3 cm, and height = 4 cm. The text “Not to scale” is written below the cuboid.]

The dimensions of the cuboid are:

• Length (l) = 7.5 cm
• Width (w) = 2.3 cm
• Height (h) = 4 cm

Solution

First, recall the formula for the total surface area of a rectangular cuboid. \[ \text{Total Surface Area} = 2(lw + lh + wh) \] Next, substitute the given dimensions into the formula. \[ \text{Total Surface Area} = 2(7.5 \times 2.3 + 7.5 \times 4 + 2.3 \times 4) \] Calculate each multiplication. \[ 7.5 \times 2.3 = 17.25 \] \[ 7.5 \times 4 = 30 \] \[ 2.3 \times 4 = 9.2 \] Add the results of the multiplications. \[ 17.25 + 30 + 9.2 = 56.45 \] Finally, multiply the sum by 2 to find the total surface area. \[ 2 \times 56.45 = 112.9 \text{ cm}^2 \] The total surface area of the cuboid is 112.9 cm².