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What is the surface area of this cuboid with dimensions
6cm,8cm and
3cm ?

What is the surface area of this cuboid with dimensions $6 \mathrm{~cm}, 8 \mathrm{~cm}$ and $3 \mathrm{~cm}$ ?

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Scale drawings: word problems

Full solution

Q. What is the surface area of this cuboid with dimensions

6 \mathrm{~cm}, 8 \mathrm{~cm}

and

3 \mathrm{~cm}

?

Calculate Area of Faces: Calculate the area of each face of the cuboid. $\newline$ - Area of face $1$ ( $6\,\text{cm} \times 8\,\text{cm}$ ): $6 \times 8 = 48\,\text{cm}^2$ $\newline$ - Area of face $2$ ( $6\,\text{cm} \times 3\,\text{cm}$ ): $6 \times 3 = 18\,\text{cm}^2$ $\newline$ - Area of face $3$ ( $8\,\text{cm} \times 3\,\text{cm}$ ): $8 \times 3 = 24\,\text{cm}^2$
Double Area of Faces: Each face has an opposite face of the same area, so double the area of each face. $\newline$ - Total area for pairs of faces: $(48 \times 2) + (18 \times 2) + (24 \times 2) = 96 + 36 + 48$
Find Total Surface Area: Add the areas of all face pairs to find the total surface area. $\newline$ - Total surface area $= 96 + 36 + 48 = 180 \, \text{cm}^2$

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