Question

A solid cylinder has the total surface area 231 sq. cm. if its curved surface area is 2/3 of the total surface area, then the volume of the cylinder is

Answer 1

hope it helps...........

Answer 2

AnswEr:

We have ,

• Total surface area = 231 cm²
• Curved surface area = $\sf\dfrac{2}{3}\times\:TSA$

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$\implies$ TSA = 231 cm² and CSA = 154 cm².

$\implies \tt \: 2\pi \: rh + 2\pi {r}^{2} = 231 \: {cm}^{2} and \\ \tt \pi \: rh = 154 \: {cm}^{2} \\ \\ \implies \tt \: 2\pi {r}^{2} + 154 = 231 \: {cm}^{2} \: and \\ \tt \: 2\pi \: rh = 154 \: {cm}^{2} \\ \\ \implies \tt \: 2\pi {r}^{2} = 77 \: and \: 2\pi \: rh = 154 \\ \\ \implies \tt \: 2 \times \frac{22}{7} \times {r}^{2} = 77 \: and \: \\ \tt2 \times \frac{22}{7} \times r \times h = 154 \\ \\ \implies \tt \: r = \frac{7}{2} \: cm \: and \: 2 \times \frac{22}{7} \times \frac{7}{2} \\ \tt \times h = 154 \\ \\ \implies \tt \: r = \frac{7}{2} \: cm \: and \: h = 7 \: cm$

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Therefore,

$\tt \: v = \pi {r}^{2} h = \frac{22}{7} \times \frac{49}{7} \times 7 \: {cm}^{3} \\ \\ \tt = 269.5 \: {cm}^{3}$