Question

volume of a cylinder volume of a cylinder is 5544 centimetre cube its height is 16 cm find its radius and then area of its curved surface ​

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\bold{given:-}\begin{cases}\sf{Volume\:of\: cylinder=5544cm{}^{3}}\\ \sf{ Height =16cm}\end{cases}$

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

• We have to find the radius of cylinder

$\bf\underline{\underline{According\:to \: Question:-}}$

$\sf Volume=\pi r{}^{2}h\\ \\ \sf\implies 5544=\frac{22}{7}\times 16\times r{}^{2}\\ \\ \sf\implies 5544\times 7=352\times r{}^{2}\\ \\ \sf\implies 38,808=352\times r{}^{2}\\ \\ \sf\implies \cancel{\frac{38808}{352}}=r{}^{2}\\ \\ \sf\implies \sqrt{110.25}=r\\ \\ \sf\implies radius =10.5 cm$

$\boxed{\mathfrak{radius=10.5cm}}$

• Now we have to find the curve surface area of cylinder

$\boxed{\sf{Curve\:surfacs\:area\:of\: cylinder=2\pi rh}}$

$\bold{we\:have:-}\begin{cases}\sf{radius=10.5cm}\\ \sf{ Height =16cm}\end{cases}$

$\sf\underline{\underline{C.S.A=curve\: surface\:area}}$

$\sf \implies C.S.A=2\times \frac{22}{\cancel7}\times \cancel{10.5}\times 16\\ \\ \sf\implies C.S.A=2\times 22\times 1.5\times 16\\ \\ \sf\implies C.S.A=44\times 24\\ \\ \sf\implies C.S.A=1056cm{}^{2}$

$\boxed{\sf{Radius=10.5cm}}$

$\boxed{\sf{Curve\: surface\:area=1056cm{}^{2}}}$

#BAL

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