Question

The surface areas of six faces of a cuboid
are 12, 12, 36, 36, 48, 48, (all in cm2). The
volume of the solid in cm3, is​

Answer 1

Solution,

The given values are the surface areas of the six faces of a cuboid:

12, 12, 36, 36, 48, 48 cm² each.

We can take the values as follows [for one face each] :

l x b = 12 cm² ----- Equation 1

b x h = 36 cm² ----- Equation 2

l x h = 48 cm² ----- Equation 3

Now, by multiplying Equations 1, 2 and 3;

(l x b) (b x h) (l x h) = 12 x 36 x 48 cm²

= 20736 cm²

The volume of a cuboid is lbh

But the given formula is

l²b²h² = 20736 cm²

In order to find the value of lbh, we have to find the root of 20736 cm².

lbh = $\sf{\sqrt{20736}}$

lbh = 144 cm³

Therefore,

Volume of the cuboid = 144 cm³

Knowledge Bytes:

→ LSA of cuboid = 2 (lh + bh)

→ TSA of cuboid = 2 (lh + bh + lb)

→ Volume of cuboid = lbh