Question

The volume of a cuboid is $3840{cm}^3$ and the length of the cuboid is $20cm$. If the ratio of its breadth and its height is $4:3$, then the total surface area of the cuboid is

Answer 1

Given: Volume of a cuboid $=3840{cm}^3$
Ratio of its breadth and height $=4:3$
Length of the cuboid $=20cm$

Let the length, breadth and height of cuboid be $l,b$ and $h$, respectively such that $b=4x$ and $h=3x$

Since, volume of cuboid $=3840{cm}^3$
$\Rightarrow lbh=3840$
$\Rightarrow 20\times 4x\times 3x=3840$
$\Rightarrow 240x^2=3840$
$\Rightarrow x^2=\frac{3840}{240}$
$\Rightarrow x=4$
$\therefore b=4x=16cm$ and $h=3x=12cm$

Thus, total surface area of cuboid $=2(lb+bh+hl)$
$=2\left[\right(20\left)\right(16)+(16\left)\right(12)+(12\left)\right(20\left)\right]$
$=2(320+192+240)$
$=1504{cm}^2$