Question

The total surface area of a cuboid is $846c{m}^2$. Find the volume if its dimensions are in the ratio of $5:4:3$.

• A. $1500c{m}^3$
• B. $1600c{m}^3$
• C. $1260c{m}^3$
• D. $1620c{m}^3$

Answer 1

Answer: (D)

Given:

The dimensions of cuboid in the ratio is $5:4:3$

Let, $l=5x$,

$b=4x$,

$h=3x$

$\Rightarrow$ TSA of cuboid $=846$ ${cm}^2$

$\Rightarrow 2(lb+bh+hl)=846{cm}^2$

$\Rightarrow 2(5x\times 4x+4x\times 3x+5x\times 3x)=846{cm}^2$

$\Rightarrow 2({20x}^2+{12x}^2+{15x}^2)=846{cm}^2$

$\Rightarrow ({20x}^2+{12x}^2+{15x}^2)=\frac{846c{m}^2}{2}$

$\Rightarrow 47x^2=423{cm}^2$

$\Rightarrow x^2=\frac{423c{m}^2}{47}$

$\Rightarrow x^2=9c{m}^2$

$\Rightarrow x=3cm$

Now,

$l=5x=5\times 3cm=15cm$

$b=4x=4\times 3cm=12cm$

$h=3x=3\times 3cm=9cm$

Volume of cuboid $=lbh$

$=15cm\times 12cm\times 9cm$

$=1620{cm}^3$

Hence, Option D is correct.