Question

A cuboid of size 16 cm × 4 cm × 11 cm is melted and re-shaped as a cylinder of height 14 cm. Find the radius of the cylinder (Assume π = 22/7)

Answer 1

Answer:

$\rm 4 \: cm$

Step-by-step explanation:

$\rm ATQ,$

$\rm \red{Cuboid_{volume}} = \blue{Cylinder_{volume}}$

$\rm \red{lbh} = \blue{\pi r^2 h}$

$\rm \red{16×4×11} = \blue{\dfrac{22}{7} r^2× 14}$

$\rm \red{704} = \blue{\dfrac{22}{\cancel{7}} r^2× \cancel{14} \: \: 2}$

$\rm \red{704} = \blue{44r^2}$

$\rm r^2 = \dfrac{\red{704}}{\blue{44}}$

$\rm r^2 = 16$

$\rm r = \sqrt{16}$

$\rm r = 4 \: cm$

Answer 2

Given,

The length of the cuboid$\[ = 16{\rm{cm}}\]$

The breadth of the cuboid$\[ = 4{\rm{cm}}\]$

The height of the cuboid$\[ = 11{\rm{cm}}\]$

The height of the cylinder$\[ = 14{\rm{cm}}\]$

To find,

The radius of the cylinder.

Solution,

Know that the volume of a cuboid is given as $\[l \times b \times h.\]$

Know that the volume of the cylinder is given as $\[\pi {r^2}h.\]$

Understand that here the volume of the cylinder and cuboid is equal as no quantity is added or subtracted.

Therefore,

$\[\begin{array}{l} \Rightarrow l \times b \times h = \pi {r^2}h\\ \Rightarrow 16 \times 4 \times 11 = \frac{{22}}{7} \times {r^2} \times 14\\ \Rightarrow {r^2} = \frac{{16 \times 4 \times 11 \times 7}}{{22 \times 14}}\\ \Rightarrow {r^2} = \frac{{4928}}{{308}}\end{array}\]$

Solve further,

$\[\begin{array}{l} \Rightarrow {r^2} = 16\\ \Rightarrow r = \sqrt {16} \\ \Rightarrow r = 4\end{array}\]$

Hence, the radius of the cylinder is $\[4\]$cm.