Question

7. The ratio of the sides of a cuboid is 3 : 4:2. If the volume of the cuboid is 12288 cm”, find the surface area of the cuboid ​

Answer 1

Total surface area of cuboid = 3328 cm²

Answer 2

• Total surface area of cuboid = 3328 cm²

Given:

• Side of cuboid are in the ratio 3:4:2.
• Volume of cuboid = 12288 cm³

To Find:

Total Surface area of cuboid.

Let Dimension of cuboid are:

• Length = 3x
• Breadth = 4x
• Height = 2x

We know that,

$\begin{gathered}\longrightarrow \bf Volume\;of\;cuboid = lbh\\ \\ \longrightarrow \sf 12288 = 3x \times 4x\times 2x\\ \\ \longrightarrow \sf 12288 = 24x^{3}\\ \\ \longrightarrow x^{3}=\dfrac{12288}{24}\\ \\ \longrightarrow \sf x^{3}=512\\ \\ \longrightarrow \sf x = \pm 8\end{gathered}$

But we know that length cannot be negative. So x = 8.

Hence, dimension are:

• Length = 3x = 3 × 8 = 24
• Breadth = 4x = 4 × 8 = 32
• Height = 2x = 2 × 8 = 16

Now, we will calculate total surface area of cuboid.

$\begin{gathered}\longrightarrow \bf Total\;surface\;area\;of\;cuboid=2[lb+bh+hl]\\ \\ \longrightarrow \sf Total\;surface\;area\;of\;cuboid=2[24\times 32+32\times 16+16\times 24]\\ \\ \longrightarrow \sf Total\;surface\;area\;of\;cuboid=2[768 + 512+384]\\ \\ \longrightarrow \sf Total\;surface\;area\;of\;cuboid=2[1664]\\ \\ \longrightarrow \sf Total\;surface\;area\;of\;cuboid=3328\;cm^{2}\end{gathered}$

Hence, Total surface area of cuboid = 3328 cm².

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