MCQ
The surface areas of the six faces of a rectangular solid are $16, 16, 32, 32, 72$ and $72$ square centimetres. The volume of the solid, in cubic centimetres, is:
- ✓$192$
- B$384$
- C$480$
- D$2592$
✓
Answer
Correct option: A.
$192$
Since, the solid has rectangular faces.
So, we have $l × b = 16 ...(i)$
$b × h = 32 ...(ii)$
$l × h = 72 ...(iii)$
where $l, b$ and $h$ are the length, breadth and height respectively, of the solid. On multiplying Eqs. $(i), (ii)$ and $(iii)$, we get
$l × b × b × h × l × h = 16 × 32 × 72$
$\Rightarrow \mathrm{l}^2 \times \mathrm{b}^2 \times \mathrm{h}^2=36864$
$⇒ (lbh)^2= 36864$
$\therefore lbh = 192$
Hence, the volumne of the solid is $192\ cu\ cm.$
So, we have $l × b = 16 ...(i)$
$b × h = 32 ...(ii)$
$l × h = 72 ...(iii)$
where $l, b$ and $h$ are the length, breadth and height respectively, of the solid. On multiplying Eqs. $(i), (ii)$ and $(iii)$, we get
$l × b × b × h × l × h = 16 × 32 × 72$
$\Rightarrow \mathrm{l}^2 \times \mathrm{b}^2 \times \mathrm{h}^2=36864$
$⇒ (lbh)^2= 36864$
$\therefore lbh = 192$
Hence, the volumne of the solid is $192\ cu\ cm.$
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