# The curved surface area of a cone is 550 cm2. If its diameter is 14 cm, find its volume.

Given.

CSA of cone = 550 cm2

Diameter is 14 cm

Formula used/Theory.

CSA of cone = πr]

Volume of cone = πr2h

If diameter is 14 cm

Then radius is half of diameter

CSA of cone = πr[]

= × 7 × []

= 22 ×

=

Squaring both sides

h2 + 49 = 252

h2 = 625 – 49

h2 = 576

h = √576 = 24 cm

Volume of cone = πr2h

= × 7 × 7 × 24

= 8 × 7 × 22

= 1232 cm2

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