Question

19. The radius and height of a night circular cylinder are
equal. Its total surface area is 616 sq cm. Find the
following:
radius
(i) area of its base
(ii) area of curved surface.
​

Answer 1

Answer:

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Answer 2

$\huge\sf\pink{Answer}$

☞ Area of the base is 154 cm & CSA is 308 cm²

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$\huge\sf\blue{Given}$

✭ Radius & Height of a cylinder are equal

✭ TSA of cylinder is 616 cm²

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$\huge\sf\gray{To \:Find}$

◈ Area of its base & the CSA?

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$\huge\sf\purple{Steps}$

Total surface area of a cylinder is given by,

$\underline{\boxed{\sf TSA_{cylinder} = 2\pi r(r+h)}}$

Substituting the given values,

➝ $\sf TSA_{cylinder} = 2\pi r(r+h) = 616$

➝ $\sf 2 \times \pi r(r+r) = 616$

➝ $\sf 2\times \pi r(2r) = 616$

➝ $\sf 4\pi r^2 = 616$

➝ $\sf \pi r^2 = \dfrac{616}{4}$

➝ $\sf \dfrac{22}{7} r^2 = 154$

➝ $\sf r^2 = 154 \times \dfrac{7}{22}$

➝ $\sf r^2 = 49$

➝ $\sf r = \sqrt{49}$

➝ $\sf \green{r = 7 \ cm}$

Area of its base is given by,

$\underline{\boxed{\sf Area_{circle} = \pi r^2}}$

Substituting the values,

➳ $\sf Area_{circle} = \pi r^2$

➳ $\sf Area = \dfrac{22}{7} \times 7^2$

➳ $\sf Area = 22\times 7$

➳ $\sf \red{Area = 154 \ cm^2}$

CSA of a cylinder is given by,

$\underline{\boxed{\sf CSA_{cylinder} = 2\pi rh}}$

Substituting the values,

➝ $\sf CSA_{cylinder} = 2\pi rh$

»» $\sf 2\times \dfrac{22}{7} \times 7 \times 7$

»» $\sf 2\times 22 \times 7$

»» $\sf \orange{CSA = 308 \ cm^2}$

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