Question

a metal clindagel disc of base radius 28 cm and height 7 cm is melted and recast into a cylinder refill block of base radius 14 cm find the length of the cylinder kal block also find the ratio of the total surface area of the cylinder kal disc to that of the block​

Answer 1

Answer:

$\large{ \green{ \underline{ \overline{ \sf \: Note : - }}}}$

$\tt\: If \: \: an \:object \: is \: \: melted \: \: and \: \: recast \: then \:$

$\tt \: the \: volume \: \: of \: new \: \: shape \: is \: equal \:$

$\tt\: to \: the \:volume\:of\: previous\: shape .$

$\large{ \green{ \underline{ \overline{ \sf \:Given : - }}}}$

$\sf \: radius \: of \: \: disc \: = 28 \: cm$

$\sf \: height \: of \: disc \: = 7 \: cm$

$\large{ \green{ \underline{ \overline{ \sf \: Solution: - }}}}$

$\sf \: volume \: of \: disc = \pi {r}^{2} h$

$\sf : \longrightarrow \: (v) = \pi \times (28) ^{2} \times 7$

$\sf : \longrightarrow (v) = \frac{22}{7} \times (28) ^{2} \times 7$

$\sf : \longrightarrow (v) = 22 \times ( {28}^{2} ) \: \: \: \: \: .......(i)$

$\sf \: radius \: of \: cylinder \: = 14 \: cm$

$\sf \: Let \: height \: be \: (h ) \: cm</p><p>$

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

$\sf : \longrightarrow \: (v) = \pi \times (14) ^{2} \times h \: \: \: \: \: .....(ii)$

$\sf \: From \: eq. \: i \: and \: ii \: volume \: of \: both \: shapes \: be \: equal$

$\sf : \longrightarrow \: \pi \times (14) ^{2} \times h = 22 \times (28) {}^{2}$

$\sf : \longrightarrow \: h = \frac{22 \times (28 {}^{2} )}{\pi( {14)}^{2} }$

$\sf : \longrightarrow \: h = 7 \times {2}^{2}$

$\sf : \longrightarrow \: h = 28 \: cm$