Question

.
5. The radius and height of a right circular cylinder are in the ratio 2:3. Find the curved surface
area if its volume is 1617 cm ​

Answer 1

“ Curved surface area of cylinder = 462 cm². ”

Explanation :

$\bf\blue{\underline{\underline{ \mapsto Given\:that :}}}$

• Radius and height of a Cylinder are in the ratio - 2 : 3.
• Volume of cylinder - 1617 cm².

$\bf\green{\underline{\underline{ \mapsto To\:find:}}}$

• Curved surface area of cylinder.

$\bf\red{\underline{\underline{ \mapsto Formula\:used:}}}$

$\boxed{\large{\underline{\rm{\gray{ Curved\:Surface\:Area_{(Cylinder)} =2\pi rh }}}}}$

$\boxed{\large{\underline{\rm{\gray{ Volume_{(Cylinder)} =\pi r^{2}h }}}}}$

Where,

• r = radius of cylinder.
• h = height of cylinder.

$\bf\orange{\underline{\underline{ \mapsto Let:}}}$

The radius and height of the cylinder be :-

• r = 2x
• h = 3x

$\bf\pink{\underline{\underline{ \mapsto Now:}}}$

• Substitute values in volume formula.

$\sf \implies 1617 = \cfrac{22}{7} \times (2x)^{2} \times 3x$

$\sf \implies 1617 = \cfrac{22 \times 12x^{3}}{7}$

$\sf \implies x^{3} = \cfrac{\cancel{1617} \times 7}{\cancel{22} \times \cancel{12}}$

$\sf \implies x^{3} = \cfrac{343}{8}$

$\sf \implies x = \sqrt[3]{\bigg(\cfrac{343}{8}\bigg)}$

$\sf \implies x = \cfrac{7}{2}$

$\sf \implies x = 3.5$

Put the value of x.

$\sf \rightarrow r = 2x = 2(3.5) = 7$

$\sf \rightarrow h = 3x = 3(3.5) = 10.5$

$\bf\red{\underline{\underline{ \mapsto Verification:}}}$

Substitute the values of radius and height of cylinder in volume formula.

$\sf \implies \cfrac{22}{\cancel{7}} \times \cancel{7} \times 7 \times 10.5$

$\sf \implies 1617$

◼ Since, LHS = RHS.

◼ Hence, it was verified.

Now, we can find out the value of CSA of cylinder.

$\sf \implies CSA = 2 \pi rh$

• r = 7 cm.
• h = 10.5 cm.

$\sf \implies CSA = 2 \times \cfrac{22}{\cancel{7}}\times \cancel{7} \times 10.5$

$\sf \implies CSA = 462$

$\underline{\boxed{\rm{\purple{\therefore Curved\:Surface\:Area_{(Cylinder)} = 462\:cm^{2}.}}}}\:\orange{\bigstar}$

$\bf\green{\underline{\underline{ \mapsto More\:info:}}}$

Formulae related to Cylinder :-

$\tt\red{\underline{\underline{\blacksquare \: Total\:Surface\:Area_{(Cylinder)} = 2 \pi r(r + h) }}}$

$\tt\red{\underline{\underline{\blacksquare \: Curved\:Surface\:Area_{(Cylinder)} = 2 \pi rh}}}$

$\tt\red{\underline{\underline{\blacksquare \: Volume_{(Cylinder)} = \pi r^{2}h}}}$

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