The dimensions of a pool are in the ratio of 4:3:1. If its volume is $6144\ m^3$, find the total surface area of the pool.

Given:

The dimensions of a pool are in the ratio of 4:3:1.

Its volume is $6144\ m^3$.

To do:

We have to find the total surface area of the pool.

Solution:

Let the length, breadth and height of the cuboidal pool be $4x, 2x$ and $x$.

Volume of a cuboid of length $l$, breadth $b$ and height $h$ is $lbh$.

 Surface area of a cuboid of length $l$, breadth $b$ and height $h$ is $2(lb+bh+lh)$.

Therefore,

$(4x)\times(3x)\times(x)=6144$

$12x^3=6144$

$x^3=512$

$x^3=8^3$

$\Rightarrow x=8\ m$

Total surface area of the pool $=2[(4x)(3x)+(3x)(x)+(x)(4x)]$

$=12x^2+3x^2+4x^2$

$=19x^2$

$=19\times(8)^2$

$=19\times64$

$=1216\ m^2$

The total surface area of the pool is $1216\ m^2$.

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Updated on: 10-Oct-2022

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