Question

the circumference of the base of a right circular cylinder is 88cm and its height is 15cm.find tge csa and tsa

Answer 1

$\huge \mathtt{ \fbox{ \fbox{SOLUTION :}}}$

Given,

• Circumference of the base of the cylinder = 88 cm

• Height of the cylinder = 15 cm

It implies , the radius of base of the cylinder is

$\mapsto \sf \: 2\pi r = 88 \\ \\ \mapsto \sf \frac{22}{7} \times r = 44 \\ \\ \mapsto \sf r = 2 \times 7 \\ \\ \mapsto \sf r = 14 \: cm \: \: or \: \: 0.14 \: m$

Hence , radius of base of the cylinder is 14 cm

We know that, the curved surface area of the cylinder is given by

$\mathtt{ \underline{ \large \fbox{CSA \: of \: cylinder = 2πrh }}}$

Where,

Circumference of the base of cylinder = 2πr

r is the radius of the base and h is the height of the cylinder

Substitute the known values , we obtain

$\mapsto \sf CSA \: of \: cylinder = </p><p>88 \times 15 \\ \\ \mapsto \sf CSA \: of \: cylinder = 1320 \: \: {cm}^{2}$

Hence , CSA of the cylinder is 1320 cm²

in terms of SI unit ,

$\mapsto \sf CSA \: of \: cylinder = 1320 \times { ({10}^{ - 2} )}^{2} \: \: {m}^{2} \: \: \: \bigg\{ \because1 \: cm = {(10)}^{ - 2} \: m \bigg\} \\ \\ \mapsto \sf CSA \: of \: cylinder = 1320 \times {10}^{ - 4} \: \: {m}^{2} \\ \\ \mapsto \sf CSA \: of \: cylinder = \frac{132 \cancel0}{1000 \cancel0} \: \: {m}^{2} \\ \\ \mapsto \sf CSA \: of \: cylinder = \frac{132}{1000} \: \: {m}^{2} \\ \\ \mapsto \sf CSA \: of \: cylinder = 0.132 \: \: {m}^{2}$

Hence , CSA of the cylinder is 0.132 m²

We know that , the total surface area of the cylinder is given by

$\mathtt{ \large \underline{ \fbox{TSA \: of \: cylinder = 2\pi {(r)}^{2} + 2\pi rh}}}$

Where ,

CSA of the cylinder = 2πrh

r is the radius of the base and h is the height of the cylinder

Substitute the known values , we obtain

$\mapsto \sf TSA \: of \: cylinder = 2 \times \frac{22}{7} \times {(14)}^{2} + 1320 \\ \\\mapsto \sf TSA \: of \: cylinder = 44 \times2 \times 14 + 1320 \\ \\\mapsto \sf TSA \: of \: cylinder = 44 \times 28 + 1320 \\ \\\mapsto \sf TSA \: of \: cylinder = 1232 + 1320 \\ \\\mapsto \sf TSA \: of \: cylinder = 2552 \: \: {cm}^{2}$

Hence , TSA of the cylinder is 2552 cm²

In terms of SI unit ,

$\mapsto \sf TSA \: of \: cylinder = 2552 \times { ({10}^{ - 2})}^{2} \: \: {m}^{2} \: \: \: \bigg\{ \because1 \: cm = {(10)}^{ - 2} \: m \bigg\} \\ \\ \mapsto \sf TSA \: of \: cylinder = \frac{2552}{10000} \: \: {m}^{2} \\ \\ \mapsto \sf TSA \: of \: cylinder = 0.2552 \: \: {m}^{2}$

Hence , TSA of the cylinder is 0.2552 m²