Question

Find the curved surface area of a cone of radius 7cm and height is 24cm ^​

Answer 1

Given :

• Radius of Cone is 7 cm .
• Height of Cone is 24 cm .

To Find :

• Curved Surface Area of Cone .

Solution :

Firstly we will find the Slant Height (l) of the Cone :

$\longmapsto\tt{l=\sqrt{{(r)}^{2}+{(h)}^{2}}}$

$\longmapsto\tt{l=\sqrt{{(7)}^{2}+{(24)}^{2}}}$

$\longmapsto\tt{l=\sqrt{49+576}}$

$\longmapsto\tt{l=\sqrt{625}}$

$\longmapsto\tt\bf{l=25\:cm}$

Now ,

$\longmapsto\tt{Radius(r)=7\:cm}$

$\longmapsto\tt{Slant\:Height(l)=25\:cm}$

Using Formula :

$\longmapsto\tt\boxed{C.S.A\:of\:Cone=\pi{rl}}$

Putting Values :

$\longmapsto\tt{\dfrac{22}{{\not{7}}}\times{{\not{7}}}\times{25}}$

$\longmapsto\tt{22\times{25}}$

$\longmapsto\tt\bf{550\:{cm}^{2}}$

So , The Curved Surface Area of Cone is 550 cm² ..

Answer 2

$\huge\bold{\underline{Question:}}$

Find the curved surface area of a cone of radius 7cm and height is 24cm²

$\huge\bold{\underline{Answer:}}$

Given:

• Radius of the cone ( r ) = 7 cm.
• Height of the cone ( h ) = 24 cm.

To find:

Find the curved surface area of a cone

Solution:

We know that,

$\huge\bold{\boxed{\rm{\red{l² = r² + h²}}}}$

Where,

• l = slant height
• r = radius
• h = height

$\sf{\implies l² = r² + h²}$

$\sf{\implies l² = 7² + 24²}$

$\sf{\implies l² = 49 + 576}$

$\sf{\implies l² = 625}$

$\sf{\implies l = √625}$

$\boxed{\bf{\purple{⟹\:l=25}}}$

Now,

Curved surface area of cone is = $\boxed{\bf{\green{πrl}}}$

$\sf{\implies πrl =\dfrac{22}{7}×7×25\:cm²}$

$\sf{\implies 22 × 25\:cm²}$

$\boxed{\sf{\pink{⟹\:550\:cm²}}}$

Therefore,the curved surface area of a cone is 550 cm²

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