Question

if the volume of cuboid is 640 cm³, its length is doubled then its breadth and its height 5 cm, find the length and breadth. ​

Answer 1

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Answer 2

$\huge\mathbb{\underline{\underline{QUESTION:-}}}$

If the volume of cuboid is 640 cm³, its length is doubled then its breadth and its height 5 cm, find the length and breadth.

$\huge \bf\red{\mid{ \overline {\underline{SOLUTION:-}}}\mid}$

$\huge\underline{\blue{\bold{GIVEN:-}}}$

Volume of Cuboid = $\sf 640cm{}^{3}$

Breadth :- ?

Length= 2breadth

Height =5 cm

$\bf{\underline{Volume\:of\: cuboid= Length×breadth×Height}}$

Let the breadth be x

then length is 2x ..

Now according to question:-

$\sf Volume\:of\:cuboid=L×B×H$

$\sf\longrightarrow 640 =x×2x×5\\ \sf\longrightarrow \frac{640}{5}=2x{}^{2}\\ \sf\longrightarrow 128=2x{}^{2}\\ \sf\longrightarrow \frac{128}{2}=x{}^{2}\\ \sf\Rightarrow 64=x{}^{2}\\ \sf\longrightarrow \sqrt{64}=x\\ \sf\longrightarrow 8=x\\ \sf\implies or\: x=8$

The value of x is 8

.So we suppose the breadth be x

=> Then the breadth is 8cm

And we supposed length be 2x

=> then length =2×8 =16cm

And the Height is Given

=> 5cm

$\large \bf\red{\mid{ \overline {\underline{VERIFICATION:-}}}\mid}$

We know that :-

Volume of cuboid =Length×Breadth×Height

$\sf\longrightarrow 640cm{}^{3}= 8cm×16cm×5cm\\ \sf\longrightarrow 640cm{}^{3}= 8cm×80cm{}^{2}\\ \sf\longrightarrow 640cm{}^{3}= 640cm{}^{3}$

L.H.S=R.H.S

$\large\boxed{\purple{\bf{Length = 16cm\:breadth=8cm}}}$