Question

the CSA of a right-angled cylinder is half of the TSA. find the radius of the base of the cylinder if the total surface area is 616 cm^2

Answer 1

Step-by-step explanation:

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Answer 2

$\large\underline\pink{Given:-}$

Cylinder of Height = 4 cm

Cylinder of Radius = 3.5 cm

$\large\underline\pink{To find:-}$

Fine the ratio of the TSA and CSA of a cylinder ....?

$\large\underline\pink{Solutions:-}$

$\: \: \: \: \: \therefore \: \: Total \: \: surface \: \: area \: \: cylinder \: \: = \: \: {2} \: \pi \: r \: {({r} \: + \: {h})}$

$\: \: \: \: \: \leadsto \: \: {2} \: \times \: \frac{22}{7} \: \times \: {3.5} \: {({3.5} \: + \: {4})}$

$\: \: \: \: \: \leadsto \: \: {2} \: \times \: \frac{22}{7} \: \times \: {3.5} \: \times \: {7.5}$

$\: \: \: \: \: \leadsto \: \: {2} \: \times \: {22} \: \times \: {0.5} \: \times \: {7.5}$

$\: \: \: \: \: \leadsto \: \: {44} \: \times \: {3.75}$

$\: \: \: \: \: \leadsto \: \: {165} \: {cm}^{2}$

$\: \: \: \: \: \therefore \: \: Curved \: \: surface \: \: area \: \: of Cylinder \: \: = \: \: {2} \: \pi \: r \: h$

$\: \: \: \: \: \leadsto \: \: {2} \: \times \: \frac{22}{7} \: \times \: {3.5} \: \times \: {4}$

$\: \: \: \: \: \leadsto \: \: {2} \: \times \: {22} \: \times \: {0.5} \: \times \: {4}$

$\: \: \: \: \: \leadsto \: \: {44} \: \times \: {2}$

$\: \: \: \: \: \leadsto \: \: {88} \: {cm}^{2}$

$\: \: \: \: \: Ratio \: \: = \: \: \frac{TSA \: \: of \: \: Cylinder}{CSA \: \: of \: \: Cylinder}$

$\: \: \: \: \: \leadsto \: \: \frac{165}{88}$

$\: \: \: \: \: \: \: Hence, \\ \: \:\therefore \: \: The \: \: ratio \: \: of \: \: the \: \: TSA \: \: and \: \: CSA \: \: of \: \: a \: \: cylinder \: \: {165} \: : \: {88}$