Question

If a cylinder of radius 4 cm and height 8 cm is melted and constructed into a cone of the same radius, what will be the height of this cone?

A) 48 cm B) 24 cm C) 36 cm D) 12 cm

Answer 1

$\large\bf\underline{Given:-}$

• Radius of cylinder = 4cm
• Height of cylinder = 8cm

$\large\bf\underline {To \: find:-}$

• Height of cone.

$\huge\bf\underline{Solution:-}$

$\begin{cases} \textrm{height \: of \: cylinder = 8cm} \\ \textrm{radius \: of \: cylinder = 4cm} \end{cases}$

• ≫ Radius of cone = Radius of cylinder

$\large\: \:\:\:\underbrace { \dag\rm \: According \: to \: question}$

Cylinder is melted and constructed into a cone having same Radius as cylinder.

So,

• Volume of cylinder = volume of cone.

$\blacktriangleright \: \bf \: volume \: of \: cone = \frac{1}{3} \pi \: {r}^{2} h \\ \\ \blacktriangleright \: \bf \: volume \: of \: cylinder = \pi \: {r}^{2} h$

$\dashrightarrow \rm \: \frac{1}{3} \times \cancel \pi \times {4}^{2} \times h = \cancel \pi \times {4}^{2} \times 8 \\ \\ \dashrightarrow \rm \: \frac{1}{3} \times 16 \times h = 16 \times 8 \\ \\ \dashrightarrow \rm \: \frac{16h}{3} = 128 \\ \\ \dashrightarrow \rm \: 16h = 128 \times 3 \\ \\ \dashrightarrow \rm \: 16h = 384 \\ \\ \dashrightarrow \rm \: h = \cancel\dfrac{384}{16} \\ \\ \dashrightarrow \bf \: h = 24$

So,

• ≫ height of cone the cone is 24cm

Hence, option B) is correct✔️

Answer 2

Answer:-

$\sf{B) \ 24 \ cm \ is \ the \ correct \ option.}$

Given:

• For cylinder,

1. Radius (r)=4 cm,
2. Height (h)=8 cm.

• For cone,

1. Radius (r)=4 cm

To find:

• Height(H) of the cone.

Solution:-

$\sf{Cone \ is \ from \ by \ melting \ cylinder. }$

$\sf{Hence, \ their \ volume \ will \ be \ same.}$

$\boxed{\sf{Volume \ of \ cylinder=\pi\times \ r^{2}\times \ h}}$

$\boxed{\sf{Volume \ of \ cone=\frac{1}{3}\times\pi\times \ r^{2}\times \ H}}$

$\sf{\pi\times \ r^{2}\times \ h=\frac{1}{3}\times\pi\times \ r^{2}\times \ H}$

$\sf{\therefore{8=\frac{1}{3}\times \ H}}$

$\sf{\therefore{H=8\times3}}$

$\sf{\therefore{H=24 \ cm}}$

$\sf\purple{\tt{\therefore{The \ height \ of \ cone \ is \ 24 \ cm}}}$