Question

find the ratio between the tsa and csa of a cylinder of height 14 cm and radius 7 cm

Answer 1

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

• Cylinder of Height = 14 cm
• Cylinder of Radius = 7 cm

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

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

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

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

$\: \: \: \: \: \leadsto \: \: {2} \: \times \: \frac{22}{7} \: \times \: {7} \: {({7} \: + \: {14})}$

$\: \: \: \: \: \leadsto \: \: {2} \: \times \: \frac{22}{7} \: \times \: {7} \: \times \: {21}$

$\: \: \: \: \: \leadsto \: \: {2} \: \times \: {22} \: \times \: {7} \: \times \: {3}$

$\: \: \: \: \: \leadsto \: \: {44} \: \times \: {21}$

$\: \: \: \: \: \leadsto \: \: {924} \: {cm}^{2}$

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

$\: \: \: \: \: \leadsto \: \: {2} \: \times \: \frac{22}{7} \: \times \: {7} \: \times \: {14}$

$\: \: \: \: \: \leadsto \: \: {2} \: \times \: {22} \: \times \: {14}$

$\: \: \: \: \: \leadsto \: \: {44} \: \times \: {14}$

$\: \: \: \: \: \leadsto \: \: {616} \: {cm}^{2}$

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

$\: \: \: \: \: \leadsto \: \: \frac{924}{616}$

$\: \: \: \: \: \leadsto \: \: \frac{3}{2}$

$\: \: \: \: \: \leadsto \: \: {3} \: : \: {2}$

$\: \: \: \: \: \: \: Hence, \\ \: \:\therefore \: \: The \: \: ratio \: \: of \: \: the \: \: TSA \: \: and \: \: CSA \: \: of \: \: a \: \: cylinder \: \: {3} \: : \: {2}$

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Answer 2

Given ,

• The height and radius of cylinder are 14 cm and 7 cm

We know that ,

The CSA of cylinder is given by

CSA = 2πrh

Thus ,

$\sf \mapsto CSA = 2 \times \frac{22}{7} \times 7 \times 14 \\ \\ \sf \mapsto CSA =44 \times 14 \\ \\ \sf \mapsto CSA =616 \: \: {cm}^{2}$

Now , the TSA of cylinder is given by

TSA = 2πrh + 2π(r)²

Thus ,

$\sf \mapsto TSA =616 + 2 \times \frac{22}{7} \times {(7)}^{2} \\ \\ \sf \mapsto TSA =616 + 44 \times 7 \\ \\ \sf \mapsto TSA =616 + 308 \\ \\ \sf \mapsto TSA = 924 \: \: {cm}^{3}$

Thus ,

The ratio of TSA and CSA of cylinder will be

$\Rightarrow \frac{TSA \: of \: cyilnder}{CSA \: of \: cyilnder} = \frac{924}{616} \\ \\ \Rightarrow \frac{TSA \: of \: cyilnder}{CSA \: of \: cyilnder} = 1.5$

Therefore ,

• The ratio of TSA and CSA of cylinder is 1.5