Question

if area of circle is same as curved surface area of cylinder. if curved surface area of cylinder is 154cm square . find diameter of circle.
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Answer 1

Step-by-step explanation:

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Since curved surface area of a cyclinder = 154 cm2 [given]

Total surface area of cyclinder = 3 × curved surface area

2πrh + 2πr2 = 3 × 154

154 + 2πr2 = 462

2πr2 = 462 - 154 = 308

r2 = 308 × 7 / 2 × 22 = 49

r = 7 cm

Now, 2πrh = 154

2 × 22 / 7 × 7 × h = 154

h = 154 / 44 = 3.5 cm

∴ Volume of cyclinder = πr2h

= 22 / 7 × 7 × 7 × 3.5 = 539 cm3

Answer 2

Answer:

$\pi {r}^{2} = \pi \: {r}^{2} h \\ \\ \pi \: {r}^{2} h = 154 \: {cm}^{2} \\ \\ \pi \: {r}^{2} = 154 \\ \\ {r}^{2} = 154 \times \frac{7}{22} \\ \\ {r}^{2} = 7 \times 7 \\ \\ r = 7 \: cm \\ \\ diameter = 2 \times radius \\ \\{ \huge { \boxed{ d = 14 \: cm}}}$