Question

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

Answer 1

Given that radius of cone = 12320cm^2.

We know that curved surface area of a cone = pirl.

GIven that curved surface area of a cone = 12320.

pirl = 12320

22/7 * 56 * l = 12320

22 * 8 * l = 12320

176l = 12320

l = 12320/176

  = 70.


We know that height of the cone h = $\sqrt{l^2 - r^2}$

                                                           = $\sqrt{70^2 - 56^2}$

                                                           = $\sqrt{4900 - 3136}$

                                                           = $\sqrt{1764}$

                                                           = 42.


Therefore the height of the cone = 42m.


Hope this helps!

Answer 2

Hi

Radius of the cone ( r ) = 56 cm

Let the height = h cm

Slant height = l cm

CSA of the cone = 12320 cm²

π rl = 12320

( 22/7 ) × 56 × l = 12320

l = ( 12320 × 7 ) / ( 56 × 22 )

l = 70 cm

l² = r² + h²

h² = l² - r²

= 70² - 56²

= ( 70 + 56 ) ( 70 - 56 )

= 126 × 14

= 14 × 3 × 3 × 14

h = √ ( 14 × 14 ) × ( 3 × 3 )

h = 14 × 3

h = 42 cm


I hope this helps you.

:)