Question

a solid cylinder has total surface area of 462 square cm It is curved surface area is one by third of its total surface area find the volume of cylinder

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Answer 1

volume of cylinder is 44

Answer 2

AnswEr:

Let r be the radius of the base and h be the height of the cylinder. Then,

• Total surface area = 2πr ( h + r ) cm²
• Curved surface area = 2πrh cm²

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We have ,

Curved surface area = $\tt\dfrac{1}{3}(Total\:surface\:area)$

= $\tt\dfrac{1}{3}\times462\:cm^2$

$\implies$ $\tt\green{2\pi\:rh=154\:cm^2}$ _____________ (i)

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Again,

$\qquad\sf\red{Total\:surface\:area=462\:cm^2}$

→2πrh + 2πr² = 462

→154 + 2πr² = 462

→$\sf{2\times}$$\sf\dfrac{22}{7}\times\:r^2$

→ 462 - 154

→ r² = 49 = r = 7 cm

From (i) we have,

$\sf{2\times}$$\sf\dfrac{22}{7}\times7\times\:h=154$

→h = $\tt\dfrac{7}{2}cm$

Hence, Volume of the cylinder = πr²h

= $\tt\dfrac{22}{7}\times7^2\times$$\tt\dfrac{7}{2}cm^3=539\:cm^3$