The base radius of an ice cream cone is 3.5 cm and the slant height is 6.5 cm. what is the capacity of the ice cream cone and its surface area (to the nearest hundredth)?

The formula of cone's capacity is V = (1 / 3) (pi x r x h)
we know that r = 3.5, we must find h, the slant height is H=6.5, applying pythagorean theorem  h ^2 = H^2, so h= sqrt (H^2 -  r^2)
h =  sqrt (6.5^2 - 3.5^2) = 5.47
 finally, V = (1 / 3)  (3.14 x 3.5 x 5.47) = 20.03 cm^3
 the surface are is A = pi x r x H = 71.43 cm^2