Question

The surface area of a cuboid is $164c{{m}^{2}}$, and length and height of the cuboid is $10cm$and $4cm$respectively. What will be the volume of the cuboid?
(a) $120c{{m}^{2}}$
(b) $100c{{m}^{2}}$
(c) $100c{{m}^{2}}$
(d) None of the above.

Answer 1

Hint: This is a question based on volume and surface area of cuboid. In this question, the surface area, length and height of the cuboid is given, and by using formula we can calculate the breadth of the cuboid. Then by using the formula of volume, we can calculate the volume of the cuboid.
Formula used –
$S=\left( lb+bh+lh \right)$
$V=lbh$
where, $l,b,h$ are the length , breadth and height of the cuboid respectively, and $S$ and $V$ are the surface area and the volume of the cuboid.

Complete step-by-step answer:
Surface area: Surface area is an area of sheet that can cover all body or phases of any shape or thing, like the surface area of a cuboid is the sum of area of all six phases of cuboid.
Volume: Volume is a measurement of [lace that can be occupied by a body, like if any body occupies $Vc{{m}^{2}}$ in the environment, then its volume is $Vc{{m}^{2}}$.

Now we can show a cuboid as below –

Let us assume that length of cuboid is $l$ cm, breadth is $b$ cm, height is $h$ cm, surface area is \[Sc{{m}^{2}}\] and volume is \[Vc{{m}^{2}}\].
Given in the question is –
$l=10cm$
$h=4cm$
$S=164c{{m}^{2}}$

Now by using formula of surface area –
$S=2\left( lb+bh+lh \right)$
$\Rightarrow 164c{{m}^{2}}=2\left\{ 10b+b4+\left( 10\times 4 \right) \right\}$
$\Rightarrow \dfrac{164}{2}=\left\{ 10b+4b+40 \right\}$
$\Rightarrow 82-41=14b$
$\Rightarrow 42=14b$
$\Rightarrow b=\dfrac{42}{14}$
$\Rightarrow b=3cm$.
So, the breadth of the cuboid is $3cm$.

Now, by using the formula of volume of cuboid –
$V=lbh$
$\Rightarrow V=\left( 10cm \right)\left( 3cm \right)\left( 4cm \right)$
$\Rightarrow V=\left( 10\times 3\times 4 \right)c{{m}^{3}}$
$\Rightarrow V=120c{{m}^{3}}$

So, the correct answer is “Option A”.

Note: (i) In this question, students should take care of silly mistakes like in surface area’s formula, we have to use $S=2\left( lb+bh+lh \right)$, but students use $S=\left( lb+bh+lh \right)$, which is wrong.
(ii) Students may make mistakes in calculation like multiplication in calculating volume or in formula of surface area calculation.