Question

perimeter of base of a cylinder is 5cm and its curved surface area is 10cm2 ,then the height of the cylinder is a)50cm b)15cm c)2cm d)5cm​

Answer 1

$\bf \underline{ \underline{\maltese\:Given} }$

$\sf \implies P erimeter \: of \: base \: of \: a \: cylinder = 5 \: cm$

$\sf \implies Curved \: surface \: area = 10 \: cm^{2}$

$\bf \underline{ \underline{\maltese \: To \: find } }$

$\sf \implies Height \: of \: the \: cylinder = \: ?$

$\bf \underline{ \underline{\maltese \: Solution } }$

$\sf \underline{First \: of \: all \: find \: the \: radius \: of \: the \: cylinder. }$

$\sf Perimeter \: of \: cylinder = Circumference$

$\implies \sf Circumference = 2\pi r$

$\sf \longrightarrow Note : \: Value \: of \: \pi = \dfrac{22}{7}$

$\bf \underline{So},$

$\implies \sf 5 = 2 \times \dfrac{22}{7} \times r$

$\implies \sf r = \dfrac{5\times 7}{2 \times 22}$

$\implies \sf r = \dfrac{35}{44}$

$\sf Thus, \: radius = \dfrac{35}{44} \: cm$

$\sf \underline{Now, find \: the \: height \: of \: cylinder. }$

$\implies \sf C.S.A = 2\pi rh$

$\bf \underline{Where},$

$\sf \implies Value \: of \: \pi = \dfrac{22}{7}$

$\sf \implies r = radius$

$\sf \implies h = height$

$\sf \underline {Substituting \: the \: values},$

$\implies \sf 10 = 2 \times \dfrac{22}{7} \times \dfrac{35}{44} \times h$

$\implies \sf h = \cancel \dfrac{10 \times 44 \times 7}{35 \times 22 \times 2} = 2$

$\implies \sf h = 2 \: cm$

$\underline{ \boxed{ \bf \red{Therefore, \: height \: of \: the \: cylinder = 2 \: cm}}}$