Question

How many solid cylinder of radius 6cm and height 12cm can be made by melting a solid sphere of radius 18cm? L. 6. measuration

Answer 1

GIVEN :-

• Radius of solid cylinder = 6 cm

• Height of solid cylinder = 12 cm

• Radius of solid sphere = 18 cm

TO FIND :-

• Number of solid cylinders.

SOLUTION ;-

Let,

Number of solid cylinder = n

$\bullet\bf \ Volume \ of \ a \ solid \ cylinder = \pi r^2h$

$\longrightarrow\sf \pi \times 6 ^ 2 \times 12 \\\\\longrightarrow \pi \times 36 \times 12 \\\\\longrightarrow\bf 432 \pi$

$\bullet\bf \ Volume \ of \ solid \ sphere = \dfrac{4}{3} \pi r^3$

$\longrightarrow\sf \dfrac{4}{3} \times \pi \times 18 \times 18 \times18 \\\\\longrightarrow4 \times \pi \times 18 \times 18 \times 6 \\\\\longrightarrow \bf 7776 \pi$

According to the question,

Volume of solid sphere = n × Volume of a solid cylinder

$\longrightarrow \sf 7776 \pi =n \times 432 \pi \\\\\longrightarrow n = \dfrac{7776\pi}{432\pi} \\\\\longrightarrow n = \dfrac{18 \times 432 }{432} \\\\\longrightarrow\bf n = 18$

Number of solid cylinders = 18