Question

The length, breadth and height of a cuboid are in the ratio 5 : 4 : 2 and the total surface area is $1216c{m}^2$, then the volume of the cuboid is

• A. $2460c{m}^3$
• B. $2560c{m}^3$
• C. $2660c{m}^3$
• D. $2700c{m}^3$

Answer 1

The correct option is B $2560c{m}^3$

Consider a given The given The length, breadth and height of a cuboid are in the ratio $5:4:2$ and the total surface area is $1216c{m}^2$,

Let, the dimension of cuboid are $l=5x,b=4x$ and $h=2x$

Now, the surface area of cuboid $=2(5x\times 4x+4x\times 2x+2x\times 5x)=76x^2$

Now,

$76x^2=1216$

$x^2=16$

$x=4$

Dimensions of cuboid are,

$l=5x=5\times 4=20cm,b=4x=4\times 4=16cm$

$h=2x=2\times 4=8cm$

Volume of cuboid$=l\times b\times h=20\times 16\times 8=2560c{m}^3$

Hence, this is the answer.