Question

Find the height of a right circular cylinder whose curved surface area is 616 cm2 and diameter of the base is 14 cm.​

Answer 1

Answer :-

$\:\large{\boxed{\sf{Firstly,\;let's\;understand\;the\;concept\;used\;:-}}}$

Here the concept used is the CSA of Cylinder has been used. We see we are given the diameter of base of cylinder. From this we can find its radius. And we can apply this in the formula of CSA of Cylinder. From this we can find the height of the cylinder.

Let's do it !!

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★ Formula Used :-

$\:\\\large{\boxed{\sf{CSA\;of\;Cylinder\;\;=\;\;\bf{2 \pi rh}}}}$

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★ Question :-

Find the height of a right circular cylinder whose curved surface area is 616 cm² and diameter of the base is 14 cm.

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★ Solution :-

Given,

» Diameter of base of cylinder = d = 14 cm

» Radius of base of cylinder = r = ½ × d = 7 cm

» CSA of Cylinder = 616 cm²

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~ For the Height of Cylinder :-

$\:\\\qquad\large{\sf{:\Longrightarrow\;\;\:CSA\;of\;Cylinder\;\;=\;\;\bf{2\:\times\:\dfrac{22}{7}\:\times\:rh}}}$

$\:\\\qquad\large{\sf{:\Longrightarrow\;\;\:616\;cm^{2}\;\;=\;\;\bf{2\:\times\:\dfrac{22}{7}\:\times\:14\:\times\:h}}}$

$\:\\\qquad\large{\sf{:\Longrightarrow\;\;\:h\;\;=\;\;\bf{\dfrac{616\:\times\:7}{22\:\times\:2\:\times\:14}\:\;=\:\;\underline{\underline{7\;\;\;cm}}}}}$

$\:\\\large{\underline{\underline{\rm{Thus,\;height\;of\;the\;cylinder\;is\;\;\boxed{\bf{7\;\;cm}}}}}}$

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★ More to know :-

• Volume of Cylinder = πr²h

• Volume of Cone = ⅓ × πr²h

• Volume of Cube = (Side)²

• Volume of Cuboid = Length × Breadth × Height

• Volume of Hemisphere = ⅔ × πr³

Answer 2

Question :

Find the height of a right circular cylinder whose curved surface area is 616 cm² and diameter of the base is 14 cm.

Answer :

Given,

• Curved surface area of right circular cylinder is 616 cm²
• Diameter of the base is 14 cm.

To find,

• Height of the right circular cylinder.

Formula used,

• Radius = $\dfrac{Diameter}{2}$

• Curved surface area of right circular cylinder = 2${\pi}$rh

Solution,

Firstly, in the question they have gave us the diameter, but according to the formula we need radius, so let's convert diameter into radius.

${\implies}$ Radius = $\dfrac{Diameter}{2}$

${\implies}$ Radius = $\dfrac{14}{2}$

${\implies}$ Radius = 7 cm

So we got the value of radius, now let's find out the height of the right circular cylinder.

${\implies}$ Curved surface area of right circular cylinder = 2${\pi}$rh

${\implies}$ 616 = 2 $\times$ $\dfrac{22}{7}$ $\times$ 7 $\times$ h

${\implies}$ h = 616 $\times$ 7/2 $\times$ 22 $\times$ 14

${\implies}$ h = 4312/616

${\implies}$ h = 7 cm

Therefore, the height of right circular cone is 7 cm.