Question

find the height of a cylinder when its volume is =1650 cm cube and radius = 5 cm




explain step by step​

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\bold{Given:-}\begin{cases}\sf{A\:\: cylinder}\\ \sf{Volume=1650cm{}^{3}}\\ \sf{radius=5cm}\end{cases}$

$\huge\sf{To\:Find:-}$

• The height of cylinder

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

$\bf\underline{\underline{Step\:By\: step\: Explanation:-}}$

$\sf\implies Volume=\pi r{}^{2}h\\ \\ \tt\:\:\implies \:\:take\: \pi =\frac{22}{7}\\ \\ \sf\implies 1650=\frac{22}{7}\times (5){}^{2}h\\ \\ \sf\implies 1650=\frac{22}{7}\times 25h\\ \\ \sf\implies 1650\times 7=22\times 25h\\ \\ \sf\implies 11550=550h\\ \\ \sf\implies \cancel{\frac{11550}{550}}=height\\ \\ \sf\implies 21=height\\ \\ \tt\implies \:\:or \: height=21cm$

• The height of cylinder is 21cm

• Lets verify our answer is correctly or not

• put the value of h in the formula if L.H.S=R.H.S then our answer is correct

$\large\boxed{\mathtt{\pink{VERIFICATION:-}}}$

$\bold{we\:have:-}\begin{cases}\sf{Volume=1650cm{}^{3}}\\ \sf{radius=5cm}\\ \sf{height=21cm}\end{cases}$

$\sf Volume\:of\: cylinder=\pi r{}^{2}h\\ \\ \tt\implies 1650=\frac{22}{7}\times (5cm){}^{2}\times 21cm\\ \\ \tt\implies 1650=\frac{22}{\cancel7}\times 25cm\times \cancel{21}cm\\ \\ \tt\implies 1650=22cm\times 25cm\times 3cm\\ \\ \tt\implies 1650= 66cm{}^{2}\times 25cm\\ \\ \tt\implies 1650cm{}^{3}=1650cm{}^{3}$

$\:\:\: \bf L.H.S=R.H.S\:\:\:\:\:\mathtt{\underline{hence\:\: verified!!}}$

$\boxed{\sf{\purple{Height\:of\: cylinder=21\:cm}}}$

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