A right cone has a radius of 4 mm, and a surface area of 176 mm2.
a) Determine the lateral area of the cone.
b) Determine the volume of the cone.
πr(r+s) = 176
16π + πrs = 176
so the lateral area is 176-16π
that makes the height
h = √(s^2 - r^2)
and the volume
v = 1/3 πr^2 h = 1/3 π * 16 √((4/π(11-π))^2 - 16) = 64/3 √(121-22π)