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Maths / Surface Area and Volume / Lateral Surface Area of a Cylinder

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Lateral Surface Area of a Cylinder

Lateral surface area of cylinder: The curved surface joining the two bases of a right circular cylinder is called its lateral surface.

The lateral surface area of cylinder = $small 2pi rh ; sq.;units$

Illustration: The curved surface area of a right circular cylinder of height 14 cm is $88;cm^{2}$ . Find the diameter of the base of the cylinder.

Solution: Let r be the radius and h be the height of the cylinder.

Then, $2pi rh=88$

$small 2times frac{22}{7}times rtimes 14=88$

$88r =88$

then r = 1 cm

Diameter of cylinder = 2 cm

Illustration: The diameter of a roller 120 cm long is 84 cm. If it takes 500 complete revolutions to level a playground, determine the cost of levelling it at the rate of 30 paise per square meter .

Solution: Clearly, the roller is a right circular cylinder of height h = 120 cm and radius of its base = r = 42 cm

So, area covered by the roller in one revolution = Curved surface area of the roller

$=2times frac{22}{7}times 42 times 120$

$=31680;cm^{2}$

So, area covered by the roller is 500 revolutions $=(31680times 500);cm^{2}$

$=frac{(31680times 500)}{100times 100};m^{2}$

$=1584;m^{2}$

Hence, the cost of levelling the playground = $=Rs;1584times frac{30}{100};m^{2}$

$=Rs;475.20$

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Lateral Surface Area of a Cylinder

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