Choose the correct answer from the given four options: A solid pi… - Vidyadip

MCQ

Choose the correct answer from the given four options: A solid piece of iron in the form of a cuboid of dimensions $49\ cm \times 33\ cm \times 24\ cm$, is moulded to form a solid sphere. The radius of the sphere is:

✓
$ 21\ cm$
B
$23\ cm$
C
$ 25\ cm$
D
$19\ cm$

✓

Answer

Correct option: A.

$ 21\ cm$

Given, dimenions of the cuboid $= 49\ cm \times 33\ cm \times 24\ cm$
$\therefore$ Volume of the cuboid $= 49 \times 33 \times 24 = 38808 \ cm ^3$
[$\because$ volume of chboid $=$ lenth $\times $ breadth $\times $ height$]$
Let the radius of the sphere is $r$, then
Volume of the sphere $=\frac{4}{3}\pi\text{r}^3$
$\Big[\because\text{volume of the sphere}=\frac{4}{3}\pi\times(\text{radius})^3\Big]$
According to the question,
Volume of the sphere $=$ Volume of the chboid
$\Rightarrow\ \ \frac{4}{3}\pi\text{r}^3=38808$
$\Rightarrow\ \ 4\times\frac{22}{7}\text{r}^3=38808\times3$
$\Rightarrow\ \ \text{r}^3=\frac{38808\times3\times7}{4\times22}=441\times21$
$\Rightarrow\ \ \text{r}^3=21\times21\times21$
$\therefore\ \ \text{r}=21\text{cm}$
Hence, the radius of the sphere is $21\ cm.$

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