Question

The length, breadth and height of a rectangular solid are in the ratio 5 : 4 : 2. If the total surface area is 1216 $c{m}^2$, find the length, the breadth and the height of the solid. Also, find the volume of the solid.

Answer 1

Consider the dimensions of the solid be 5x, 4x and 2x
Total Surface Area = 2(lb + bh + hl) = 1216
Substituting the values
$2(20x^2+8x^2+10x^2)=1216x^2=\frac{1216}{76}{x}^2=16x=4cm\text{So we get}5x=5\times 4=20cm4x=4\times 4=16cm2x=2\times 4=8cm$
Hence, the dimensions are 20 cm, 16 cm and 8 cm.
Now,
Volume = lbh
$=20\times 16\times 8=2560c{m}^3$