Question

The curved surface of a cone is 204.1 sq cm and it's radius is 5 cm . What is its perpendicular height ? ( IT =3.14)​

Answer 1

Given:-

• Curved Surface Area of the cone is 204.1 cm²
• Radius of cone = 5 cm

To Find:-

• Perpendicular height of the cone.

Note:-

• Refer to the attachment attached.

Solution:-

From the attachment we can clearly see:-

• OC = 5 cm (Radius)

We know,

$\dag\underline{\pink{\boxed{\blue{\bf{Curved\:Surface\:Area\:of\:Cone = \pi rl}}}}}$

Hence,

$\sf{204.1 = 3.14\times 5 \times l}$

$= \sf{\dfrac{204.1}{3.14 \times 5} = l}$

$= \sf{\dfrac{65}{5} = l}$

$= \sf{l = 13}$

$\underline{\boxed{\red{\bf{\therefore\:The\:Slant\:height\:of\:the\:Cone\:is\:13\:cm}}}}$

Now,

We have,

• OC = 5 cm
• AC = 13 cm

$\sf{\underline{\underline{\pink{According\:to\:Pythagoras\:Theorem}}}}$

(AO)² = (AC)² - (OC)²

$= \sf{AO = \sqrt{(AC)^2 - (OC)^2}}$

$= \sf{AO = \sqrt{(13)^2 - (5)^2}}$

$= \sf{AO = \sqrt{169 - 25}}$

$= \sf{AO = \sqrt{144}}$

$= \sf{AO = 12}$

$\underline{\pink{\boxed{\green{\bf{\therefore\:The\:length\:of\:perpendicular\:height\:of\:the\:cone\:is\:12\:cm}}}}}$

______________________________________

Answer 2

Given :-

• Curverd Surface Area of the cone is 204.1 cm².
• Radius of cone = 5 cm

To find :-

• Find the Perpendicular height of the cone.

★ $\large\underline{\frak{As \: we \: know \: that, }}$

$\large\dag$Formula Used

• $\boxed{\bf{Curverd~Surface ~Area ~of~ Cone~ =~ πrl}}$

Solution :-

• OC = 5cm ( Radius )

$\large\dag$ Hence forth,

:$\implies$204.1 = 3.14 × 5 × L

$~~~~~$:$\implies$$\large{\sf{\frac{204.1}{3.14 \: \times \: 5}}}$= L

$~~~~~~~~~~$:$\implies$$\large{\sf{\frac{65}{5}}}$= L

$~~~~~~~~~~~~~~~$:$\implies$${\cancel{\dfrac{65}{5}}}$= L

$~~~~~~~~~~~~~~~~~~~~$:$\implies$${\underline{\boxed{\pink{\frak{L~=~13}}}}}$★

$\large\dag$ Hence,

• The Slant height of the Cone is = $\large{\rm{13~cm}}$

Now,

• $\leadsto$OC = 5cm
• $\leadsto$AC = 13cm

★ According to Pythagoras Theorem,

:$\implies$(AO)² = (AC)² - (OC)2

$~~~~~$:$\implies$AO = ${\sf{\sqrt{(AC {)}^{2} \: - \: (OC {)}^{2} } }}$

$~~~~~~~~~~$:$\implies$AO = ${\sf{\sqrt{(13{)}^{2} \: - \: (5 {)}^{2} } }}$

$~~~~~~~~~~~~~~~$:$\implies$${\sf{\sqrt{169 \: - \: 25} }}$

$~~~~~~~~~~~~~~~~~~~~$:$\implies$AO = ${\sf{\sqrt{144} }}$

$~~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$${\underline{\boxed{\pink{\frak{AO~=~12}}}}}$★

$\large\dag$ Hence Verified,

• The Length of Perpendicular Height of the Cone is $\large\underline{\rm{12~cm}}$