Question

If a cubical metal of dimensions 44 cm $\times$ 30 cm $\times$ 15 cm was melted and cast into a cylinder of height of 28 cm, then what is its radius?

• A. $15$
• B. $15\sqrt{3}$
• C. $3\sqrt{6}$
• D. $5\sqrt{3}$

Answer 1

The correct option is A $15$

$\Rightarrow$ Dimension of cuboid $=44cm\times 30cm\times 15cm$

$\Rightarrow$ Height of a cylinder $\left(H\right)=28cm$

According to the question,

$\Rightarrow$ Volume of a cuboid $=$ Volume of cylinder.

$\Rightarrow$ $l\times b\times h=\pi \times r^2\times H$

$\Rightarrow$ $44\times 30\times 15=\frac{22}{7}\times \left(r^2\right)\times 28$

$\Rightarrow$ $44\times 30\times 15=22\times 4\times r^2$

$\Rightarrow$ $r^2=\frac{44\times 30\times 15}{22\times 4}$

$\Rightarrow$ $r^2=225c{m}^2$

$\therefore$ $r=15cm$