Question

the breath of a cuboid is two-third of its length and height is one third of its length. If the volume of cuboid is 3072cm. find the base area of the cuboid

Answer 1

Given : The breadth of a cuboid is $\rm \dfrac{2}{3}$ of its length and height is $\rm \dfrac{1}{3}$ of its length. The volume of the given cuboid is $\rm 3072cm^3.$

To find : The base area of the cuboid.

$\qquad$______________

Let the length of the cuboid be $\rm x$ cm.

So, according to the question :

$\:$

★ Breadth of the cuboid = $\rm \dfrac{2}{3}$ of Length

$\rm\qquad \dashrightarrow \: b = \dfrac{2x}{3} \: cm$

$\:$

★ Height of the cuboid = $\rm \dfrac{1}{3}$ of Length

$\rm \qquad \dashrightarrow \: h = \dfrac{1x}{3} \: cm$

$\:$

Here, we know the formula :

$\bf Volume_{(cuboid)}=Length ~(Breadth)~(Height)$

$\:$

Substituting the values in the formula to find the value of $\rm x:$

$\:$

$\rm \qquad \dashrightarrow \: x \bigg \lgroup \dfrac{2x}{3} \bigg \rgroup \bigg \lgroup \dfrac{1x}{3} \bigg \rgroup = 3072 \: {cm}^{3}$

$\:$

$\rm \qquad \dashrightarrow \: \bigg \lgroup\dfrac{2 {x}^{3} }{9} \bigg \rgroup = 3072 \: {cm}^{3}$

$\:$

$\rm \qquad \dashrightarrow \: 2 {x}^{ 3} =(9) \: ( 3072 \: {cm}^{3}) \:$

$\:$

$\rm \qquad \dashrightarrow \: 2 {x}^{3} = 27648 \:cm ^{3}$

$\:$

$\rm \qquad \dashrightarrow \: {x}^{ 3} = \cancel\dfrac{27648 \: cm ^{3} }{2}$

$\:$

$\rm \qquad \dashrightarrow \:x = \sqrt[3]{13824 \: cm ^{3} }$

$\:$

$\bf \qquad \dashrightarrow \: x = 24 \: m$

Substituting the value of $\rm x$ for getting breadth and height :

$~$

★ Breadth of the cuboid = $\rm \dfrac{2}{3}~(x)$

$\rm\qquad\dashrightarrow~ 16~cm$

$~$

★ Height of the cuboid = $\rm \dfrac{1}{3}~(x)$

$\rm \qquad\dashrightarrow~ 8~cm$

Finding the base area by substituting the values :

$~$

$\rm \qquad\dashrightarrow~ Area_{(base)}=Length~(Breadth)$

$\qquad\rm \dashrightarrow~ Area=(24cm)~(16cm)$

$\bf \qquad\dashrightarrow~ Area=348~cm^2$

$\rm\therefore{\underline{ The~ base~ area~ of~the~ cuboid~ is~}}\underline{\bf 348~ cm^2.}$