Question

The height of the cone if the curved surface area of a cone is 12320 cm², if the radius of its base is 56 cm?

Answer 1

⚝ Given:-    

• ➛ The curved surface area of a cone is 12320 cm².
• ➛ the radius of its base is 56 cm.

⚝ To find:-      

• ➛ The height of the cone.

⚝ Formula Used:-      

To solve the question we will use 2 formulae,

➛ First is The curved surface area of the cone.

➛ Second is The height of the cone.

The curved surface area of the cone,

• $\Large\boxed{\underline{\tt{Curved\:surface\:area\:_{(\:CONE\:)}=\:\pi\:r\:l}}}$

Where,

• π = Pi
• r = radius of its base
• l = the slant height

The height of the cone,

$\Large\boxed{\underline{\tt{Height\:=\:\sqrt{\:(\:Lenght\:)^{2}\:-\:(\:Radius\:)^{2}} }}}$

Where,

• H = Height
• L = Lenght
• R = radius

⚝ Solution:-    

To find out the height of the cone we need a length of the cone so firstly we will find out the Lenght of the cone by substituting the values in the formula we get,

                    ______________

~Length of the cone

➛ Curved surface area of cone = πrl

➛ 12320  = 22/7 × 56 × l

➛ 12320  = 22 × 8 × l

➛ 12320  = 176 × l

➛ l = 12320/176

➛ l = 70 cm

. ° . Thus, The length of the cone is 70 cm.

                _____________

~The height of the cone

Now we will find out the Height of the cone by using the formula.

➛ Height = √ ( Lenght )² - ( Radius )²

➛ Height = √ ( 70 )² - ( 56 )²

➛ Height = √ 4900 - 3136

➛ Height = √ 1764

➛ Height = 42 cm

. ° . Thus, The height of the cone is 42 cm.

                _______________