Question

The surface area of 3 coterminous faces of a cuboid are 6, 15, 10 sq. cm respectively. Find the volume of the cuboid.
A. 30 ${cm}^{3}$ B. 20 ${cm}^{3}$ c. 40 ${cm}^{3}$ D. 35 ${cm}^{3}$

Answer 1

Hint: Coterminous means they meet at a common vertex. So this question gives us data on 3 adjacent faces that share a common vertex. We will write the formula of area for each face and then calculate volume.

Complete step-by-step answer:
Lb = 6 sq cm
bh = 15 sq cm
hl = 10 sq cm
According to the question multiplying all of them, we get
\[{l^2}{b^2}{h^2} = 6 \times 10 \times 15\]
$lbh = {\left( {6 \times 10 \times 15} \right)^{{\raise0.5ex\hbox{$\scriptstyle 1$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}}} = 30{\text{c}}{{\text{m}}^3}$
Which is the volume of the cuboid.
Hence, option A is correct.

Note: We can also use the fact that all 3 mentioned areas are different to arrive at the fast that they must be talking about lb, bh and lh. Since a cuboid is made up of only 3 unique faces, there can at max be 3 different surface areas of those faces. The numbers mentioned here are distinct, hence it has to mean lb, bh and lh faces.