Question

26. A solid metallic cylinder of radius 12 cm and height
20 cm is melted into 8 cylinders of radius 6 cm. Find
the height of the small cylinders.​

Answer 1

Given

A solid metallic cylinder of radius 12 cm and height 20 cm is melted into 8 cylinders of radius 6 cm.

To find

Height of the small cylinders

Solution

• Before melting

$\\{\bold\dag}\:{\bf{\blue{Radius\:of\:a\:cylinder = 12cm}}}$

${\bold\dag}\:{\bf{\blue{Height\:of\:a\:cylinder = 20cm}}}$

$\qquad\quad$ Volume of cylinder

$\implies\sf \pi r^2 h$

$\implies\sf \pi \times 12 \times 12 \times 20$

$\implies\sf 2880\pi \: cm^3$

$\:$____________________________________________

A solid metallic cylinder is melted into 8 cylinders of radius 6cm

• After melting

$\\{\bold\dag}\:{\bf{\red{Radius\:of\:a\:cylinder = 6cm}}}$

$\qquad\quad$Volume of 8 cylinders

$\\\implies\sf 8 \times \pi r^2 h$

$\implies\sf 8 \times \pi \times 6 \times 6 \times h$

$\implies\sf 288\pi h \: cm^3$

Volume of cylinder = volume of 8 cylinders

$\\\implies\sf 2880\pi = 288\pi h$

• Cancel π

$\\\implies\sf h = \cancel\dfrac{2880}{288}$

$\implies\sf h = 10cm$

$\therefore{\underline{\boxed{\sf{Height\:of\:the\: small\: cylinders = 10cm}}}}$

$\:$____________________________________________

Answer 2

Answer:

• Height of big solid cylinder is 12 cm.
• Height of big cylinder is 20 cm
• Big cylinder is melted in 8 small cylinders
• Radius of one small cylinder is 6 cm.

Find height of small cylinder

Solution:

Volume of cylinder =pie r square h

Volume of big cylinder:

➡️Volume=pie r square h

➡️Volume=22/7x(12)squarex20

➡️Volume=22/7x144x20

➡️Volume=22/7x2880

➡️Volume=63360/7

➡️Volume=9051.42

Volume of big cylinder is 9051.42 cm cube

Let the height of small cylinder be h

➡️Volume=pie r square hx8

➡️Volume=22/7x(6)squarexhx8

➡️Volume=22/7x36xhx8

➡️Volume=6336/7xh

➡️Volume=905.142 h

Volume of small cylinders is 905.142 h cm cube

• Now if we melt one big cylinder in 8 small cylinders will equal to total volume of 8 cylinders.

So,

Volume of big cylinder =volume of 8 small cylinders

➡️9051.42=905.142 h

➡️905.142/905.142=h

➡️h=10

Height of small cylinder is 10 cm.