Question

Height of rectangular box is 10cm Area of its four
vertical faces is 560cm? Find the perimeter of its base. ​

Answer 1

❖ Answer :–

$\frak{Given}\begin{cases}\sf{It's\:is\:\bf{cuboidal}}\sf\:in\:shape.\\\sf{Height\:of\:the\:box=\bf{10\:cm.}}\\\sf{Area\:of\:4\:walls=\bf{560\:cm².}}\end{cases}$

$\bigstar\;\underline{\bf To\:Find:-}$

• The perimeter of the base.

${\underbrace{\underline{\bf Required\:Solution:-}}}$

» In this question, the Area of the four vertical faces mean the Curved Surface Area (C.S.A.) of the cuboid.

» We would use the given height and formula for CSA,and would resolve it to get the perimeter of the cuboid.

» The perimeter of the base asked in the question is nothing else but the perimeter of rectangle. The base of a cuboid is made up of the length and the breadth.

We know :

$\odot\;\boxed{\sf CSA_{\:cuboid}=2(length+breadth)\times height}...(i)$

Also,

$\odot\;\boxed{\sf Perimeter_{\:rectangle}=2(length+breadth)}...(ii)$

Put eq(ii) into eq(i)

So,

$\colon\rarr\sf\:CSA_{\:cuboid}=Perimeter\times height$

• Put the value of CSA and height in the above equation.

$\colon \rarr \sf \: \cancel{560 \: {cm}^{2}} = perimeter \times \cancel{ 10 \: cm} \\ \\ \colon \dashrightarrow \underline{ \green \dag \: {\boxed{ \frak {\pink{perimeter = 56 \: cm}}} \: \green \dag}}$

$\therefore\;\underline{\sf The\:Perimeter\:of\:the\:base\:would\:be\:\bf{56\:cm.}}$

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