Question

A metallic cylinder with height 20 cm and the diameter of base 56 cm is melted to make smaller
cylinders of radius 7 cm and height 5 cm. How many cylinders can be made?​

Answer 1

${ \rm{ \large \underline \bold{given}}}$

${ \rm{ the \: height \: of \: a \: cylinder = 20 \: cm}}$

${ \rm{the \: diameter \: of \: base = 56 \: cm}}$

${ \rm{ \therefore \: radius = \frac{56}{2} = 28}}$

${ \rm{\therefore volume = \pi {r}^{2} h}}$

${ \rm{ = \frac{22}{7} \times 28 \times 28 \times 20}}$

${ \rm{ = {22 \times 28 \times 4 \times 20} }}$

${ \rm{ = {49280} \: {cm}^{3} }}$

${ \rm{so \: the \: volume \: is \: 16246.6 \: {cm}^{3}}}$

${ \rm{now \: the \: radius \: of \: smaller \: cylinder = 7 \: cm}}$

${ \rm{ and \: height = 5 \: cm}}$

${ \rm{ \therefore volume \: of \: each \: cylinder = \pi {r}^{2}h}}$

${ \rm{ = \frac{22}{7} \times {7} \times7 \times 5}}$

${ \rm{ = {22 \times 7 \times 5} }}$

${ \rm{ = {770} \: {cm}^{3} }}$

${ \rm{no.of \: cylinders = \frac{volume \: of \: original \: cylinders}{volume \: of \: smaller \: cylinder} }}$

${ \rm{ = \frac{49820}{770} }}$

${ \rm{ = 64}}$

${ \rm{ \large{so \: the \: no.of \: cylinders \: are \: 64}}}$

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$\boxed{\large \underline \mathfrak \purple{more \: information}}$

${ \rm{ area \: of \: cross \: section = \pi {r}^{2} }}$

${ \rm{perimeter = 2 \pi r}}$

${ \rm{curved \: surfce \: area = 2 \pi rh}}$

${ \rm{total \: surface \: area = 2 \pi r(h + r)}}$

${ \rm{volume = \pi {r}^{2} h}}$