Question

A right circular cone having radius 5 cm and height 12 cm is given. The curved surface area of the cone is ki​

Answer 1

Answer :

• curved surface area of cone is 204.286 cm²

Given :

• radius is 5cm
• height is 12cm

To find :

• curved surface area

Solution:

As we know that :

• slant height = √r² + h²

⇢ slant height = √5² + 12²

⇢ √25 + 144

⇢ √169 cm

⇢ 13cm

Now we have to find the curved surface area :

As we know that :

• curved surface area = πrl

where r is 5cm and l is 13cm

⇢ 22/7 × 5 × 13

⇢ 204.286 cm²

Curved surface area of cone is 204.286cm²

More Explanation :

• Volume of cone = πr²h/3
• surface area of cone = πr(r + √h² + r²
• Lateral surface area of cone = πr √h² + r²
• slant height = √r² + h²

Answer 2

$\boxed{\fcolorbox{red}{lightblue}{Given}}$

• A right circular cone having radius 5 cm and height 12 cm.

$\boxed{\fcolorbox{red}{lightblue}{To \: find}}$

• The curved surface area of the cone.

$\boxed{\fcolorbox{red}{lightblue}{Solution}}$

We know that,

The slant height of a cone

$\sf{ {l}^{2} = r + h}$

$\sf{\implies l = \sqrt{ {r}^{2} + {h}^{2} } }$

$\sf{\implies l = \sqrt{ {5}^{2} + {12}^{2} } }$

$\sf{\implies l = \sqrt{25 + 144} }$

$\sf{\implies l = \sqrt{169} }$

$\sf{\implies l = 13 }$

Therefore,the slant height of the cone is 13 cm.

Now, the curved surface area of the cone is (CSA)$\sf{</u></strong><strong><u>=</u></strong><strong><u> </u></strong><strong><u>\pi r l}$

$\</u></strong><strong><u>s</u></strong><strong><u>f</u></strong><strong><u>{\implies </u></strong><strong><u>CSA</u></strong><strong><u> = \frac{22}{7} \times 5 \times 13}$

$\sf{\implies </u></strong><strong><u> </u></strong><strong><u>CSA</u></strong><strong><u> </u></strong><strong><u>= \frac{1430}{7} }$

$\sf{\implies </u></strong><strong><u>CSA</u></strong><strong><u> = 204.28}$

Hence, the curved surface area of the cone = 204.28 cm².