Question

Two tanks are of the same capacity. The dimensions of the first tank are 32 cm, 18 cm and 7 cm. The second tank has the square base with depth 7 cm. Find the side of the square base.

Answer 1

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

$\bold{Given:-}\begin{cases}\sf{Dimensions\:of\:Two\: tank}\\ \sf{Tank\:1=>l=32cm\:,b=18cm\:,h=7cm}\\ \sf{Tank_2:- height=7cm}\end{cases}$

First find the volume of 1st tank because the volume of both tanks are equal

$\boxed{\sf{Volume\:of\: cuboid=l\times b\times h}}$

$\bf\underline{\underline{According\:To\: Question:-}}$

$\sf\implies Volume=32\times 18\times 7\\ \\ \sf\implies Volume=32\times 126\\ \\ \sf\implies Volume=4032cm{}^{3}$

$\boxed{\sf{Volume\:of\:tank=4032cm{}^{3}}}$

• Now the volume of 2nd tank is also
• $\tt\implies 4032cm{}^{3}$

$\boxed{\sf{ volume\:of\:tank_1=Volume\:of\:tank_2}}$

• We have to find the side of square base
• Let the square base be y

$\sf\implies Volume=l\times b\times h\\ \\ \sf\implies 4032=y\times 7\\ \\ \sf\implies \cancel{\frac{4032}{7}}=y\\ \\ \sf\implies 576cm{}^{2}=y$

• The square base of 2nd tank is $\sf 576cm{}^{2}$

• Now we have to find the side of square base

$\sf\underline{\underline{Area\:of\:square=side{}^{2}}}$

$\sf\implies side=\sqrt{576cm{}^{2}}\\ \\ \sf\implies side=24cm$

• Side of square base =24cm

$\boxed{\mathfrak{\purple{Side\:of\:sqiare\:base=24cm}}}$

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