Question

The lenght breadth height of a cuboid block are in the ratio 5:4:3 its surface area is1216cmsq what is the volume of the solid

Answer 1

Let the length, breadth and height of the cuboid be 5x, 4x and 3x, respectively.

$$A=2(ab+bc+ac)=2(20+12+15)x^2=1216$$

$$94x^2=1216$$

$$x=4\sqrt{\frac{38}{47}}$$

$$V=abc=(5)(4)(3)\left(4\sqrt{\frac{38}{47}}\right)^3$$

$$V=2792\ cm^3$$