Question

The curved surface area of a right circular cone is 12320cm2

. If the radius of its base is

56cm.find its height. ​

Answer 1

In the above Question, the following information is given -

The curved surface area of a right circular cone is 12320cm² .

The radius of the covlne is 56 cm .

Now , we know that -

Curved Surface area of a right circular Cone

=> πrl

Where ,

r is the radius of the cone .

l is the slant height of the cone .

l = √ [ r² + h² ]

Now ,

Substituting the given Values into the formula -

π × 56 × l = 12320

=> ( 22 / 7 ) × 56 × l = 12320

=> l = 70 cm

Now ,

l = √ [ r² + h² ]

Let the height of the given cone be x cm

=> l² = r² + h²

=> 4900 = 3136 + h²

=> h² = 4900 - 3136

=> h² = 1764 cm²

=> h =42 cm .

Hence the required height of the cone is 42 cm .... A

__________

Answer 2

Answer

• The curved surface area of a right circular cone , CSA = 12320 cm²
• Radius of its base , r = 56 cm
• Curved Surface Area of right circular cylinder , CSA = πrl

⇒ πrl =  12320

⇒ (22/7) (56)l = 12320

⇒ l = 70 cm

Now , In right circular cylinder ,

$\bold{l^2=r^2+h^2}\\\\\implies \bold{70^2=56^2+h^2}\\\\\implies \bold{4900=3136+h^2}\\\\\implies \bold{h^2=4900-3136}\\\\\implies \bold{h^2=1764}\\\\\implies \bold{\bf{\blue{h=42\;cm}}}$

Hence the height of the right circular cone is 42 cm .