Question

the surface area of three coterminous faces of cuboid are 6 cm^2 ,15 cm^2 and 10 cm^2 respectively. what is the volume of the cuboid ?

Answer 1

 Suppose l, b, h be the dimensions of the cuboid, then
 Volume of the cuboid = l* b*h

Here, l*b= 6; b*h = 15; h*l = 10.
multiply each individal surface area together we get-

(l*b*h)^2 = 6*15*10

l*b*h = sqrt(900) =30

Volume of the cuboid = l* b*h =30 cubic cm

Answer 2

Here is your answer

Area of 1st face= 6cm² (l×b)

Area of 2nd face = 15cm² (b×h)

Area of 3rd face= 10cm² (h×l)

Volume of the cuboid= l×b×h

So,

(lb)(bh)(hl) = 6×15×10

l²b²h²= 900

(lbh)²=900

lbh=√900

lbh=30cm³

Therefore, volume of the cuboid is 30 cm³