Question

The curved surface area of a cone is 12320 sq cm. if the radius of its base is 56 cm, find its height.

Answer 1

Curved Surface Area of cone = 12320 cm sq.
Radius of its base = 56 cm.
Let the Height be = h
According to question, equation formed will be>>>

 Curved surface area of cone = 12320  
        π r h + π r 2                      =  12320   
(22/7 * 56* h) + 22/7 * 56*2    =  12320 
176 * h  + 352                          =  12320 
            176 * h                          =  12320 - 352
                h                                = 11968/ 176
                h                                =  68cm

So, the height of the cone is 68cm

Answer 2

Answer:

Here, radius of base of a cone (r) = 56 cm

And, curved surface area = 12320 cm2

πrl = 12320

l = 12320πr

= 12320×722×56 = 70 cm

Again, we have

r2 + h2 = l2

h2 = l2 – r2 = 702 – 562

= 4900 – 3136 = 1764

h = √1764 = 42 cm

Hence, the height of the cone is 42 cm.