The surface areas of the three coterminous faces of a cuboid are $6,15$ and $10 c{m}^2$respectively. The volume of the cuboid is:

Volume and Surface Area

1. Cube:

$V=a^3$

$LSA=4a^2$

2. Cuboid:

$V=l\times b\times h$

$LSA=2h \left(l+b\right)$

$TSA=2lb+bh+hl$

3. Sphere:

$V=\frac{4}{3}\mathrm{\pi }{r}^3$

$LSA=4\pi r^2$

$TSA=4\pi r^2$

4. Cylinder:

$V=\pi r^{2}h$

$LSA=2\pi rh$

$TSA=2\pi rh+2\pi r^2$

5. Cone:

$V=\frac{1}{3}\mathrm{\pi }{r}^{2}h$

$LSA=\pi rl$

$TSA=\pi r\left(r+l\right)$

6. Pyramid:

$V=\frac{1}{2}\times$Area of base$\times$Height

$LSA=\frac{1}{2}\times$Perimeter of base$\times$Slant height

$TSA=\frac{1}{2}\times$Perimeter of base$\times$Slant height$+$Area of the base

7. Prism:

$V=$Base area$\times$Height

$TSA=2\times$Base area$+$Lateral surface area

8. Regular Tetrahedron:

$V=\frac{{\left(Side\right)}^3}{6\sqrt{2}}$

$TSA=\sqrt{3}\times {\left(Side\right)}^2$