Question

if the total surface area of a solid right cylinder is 880 sq.cm and it's radius is 10cm,find it's curved surface area.(take pi= 22 / 7​

Answer 1

Step-by-step explanation:

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Answer 2

$\bigstar\large\underbrace\purple{\frak{Given}}$

• Total surface area of a solid right cylinder is 880cm²
• Radius of cylinder 10cm

$\bigstar\large\underbrace\purple{\frak{To \: Find }}$

• Curved surface area of solid right cylinder
• Height of solid right cylinder

$\bigstar\large\underbrace\purple{\frak{formulas }}$

$\sf \: Curved \: surface \: area _{(cylinder)} = 2\pi r(h + r)$

$\bigstar\large\underbrace\purple{\frak{solution }}$

Given that the total surface area of a solid right cylinder is 880cm and it's radius 10cm, let height of the cylinder be h

Now,

$\sf\longmapsto Total \: surface \: area_{(solid \: right \: cylinder)} = 2\pi r(h + r)$

Putting values in formals

$\sf\longmapsto Total \: surface \: area_{(solid \: right \: cylinder)} = 2\pi r(h + r) \\ \\\sf\longmapsto 880= 2 \times \frac{22}{7} \times 10(h + 10) \\ \\ \sf\longmapsto \: h \: + 10 = \frac{88 \cancel0 \times 7}{2 \times 22 \times 1 \cancel0} \\ \\ \sf\longmapsto \: h + 10 = \frac{ \cancel{88} \times 7}{2 \times \cancel{22}} \\ \\ \sf\longmapsto \: h + 10 = \frac{4 \times 7}{2} \\ \\ \sf\longmapsto \: h + 10 = \cancel \frac{28}{2} \\ \\ \sf\longmapsto \: h + 10 = 14 \\ \\ \sf\longmapsto \: h = 14 - 10 \\ \\ \sf\longmapsto \: h \: = 4$

Hence, height of the cylinder be 4cm

________________________

Now,

We find curved surface area of a solid right cylinder

We know that,

$\sf \: Curved \: surface \: area_ {(solid \: right \: cylinder) } = 2\pi rh$

Putting values in formals

$\longmapsto\sf \: Curved \: surface \: area_ {(solid \: right \: cylinder) } = 2\pi rh \\ \\ \longmapsto\sf \: Curved \: surface \: area_ {(solid \: right \: cylinder) } = 2 \times \frac{22}{7} \times 10 \times 4 \\ \\ \longmapsto\sf \: Curved \: surface \: area_ {(solid \: right \: cylinder) } = \frac{44 \times 10 \times 4}{7} \\ \\ \longmapsto\sf \: Curved \: surface \: area_ {(solid \: right \: cylinder) } = \frac{440 \times 4}{7} \\ \\ \longmapsto\sf \: Curved \: surface \: area_ {(solid \: right \: cylinder) } = \frac{1760}{7} \\ \\ \red{ \longmapsto\sf \: Curved \: surface \: area_ {(solid \: right \: cylinder)} = 251 \frac{3}{7} {cm}^{2} }$

Hence, the curved surface area of a solid right cylinder is $\sf \: 251 {cm}^{2}$