Question

The Surface of a cuboidal wooden box is 470cm². if its length and breadth are 15cm and 8cm respectively, find its height​

Answer 1

Given : The total surface area, length and breadth of a cuboid are 470cm², 15cm and 8cm respectively.

To Find : Height of the cuboidal wooden box.

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Here

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• Length of the cuboid = 15cm
• Breadth of the cuboid = 8cm
• T.S.A of the cuboid = 470cm²

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$\underline{\boxed{\tt\purple{\bigstar \: T.S.A \: of \: a \: cuboid \: = 2(lb + bh + lh)}}}$

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Where

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• l = length
• b = breadth
• h = height

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Put the values -

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$\tt:\implies \: 470 = 2[(15 \times 8) + (8 \times h) +( 15 \times h)] \\ \\ \\ \tt:\implies \: \cancel\frac{470}{2} = 120 + 8h + 15h \\ \\ \\ \tt:\implies \: 235 = 120 + 23h \\ \\ \\ \tt:\implies \: 235 - 120 = 23h \\ \\ \\ \tt:\implies \: 115 = 23h \\ \\ \\ \tt:\implies \: h = \cancel \frac{115}{23} \\ \\ \\ \tt:\implies \: h = \underline{\boxed{\tt\purple{5cm}}}\bigstar \\ \\ \\ \sf\therefore{\underline{Hence, \: the \: height \: of \: the \: cuboidal \: box \: is \: \bold{5cm}}}$