Question

Find the radius and height of a cylinder whose tsa is 231cm and csa is 154 cm

Answer 1

TSA = 2 pi r^2 + 2pi r h

CSA = 2 pi rh

2 pi r^2 + 2pi r h = 231. eq1

2pi r h = 154. eq2

Put value of 2 pi r h in eq1

2pi r^2 + 154 = 231

2pi r^2 = 231 - 154 = 77

r^2 = 77×7 / 44 = 539 / 44

r^2 = 49 / 4

r = 7 / 2 cm

Now put value of r in eq 2

2 × 22/7 × 7/2 × h = 154

22h = 154

h = 154 / 22 = 7cm

Hence radius is 7/2cm. and height is 7cm

Thanks

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 ....?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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