a) If r1 and r2 are the radius of the cones, and thei ratio of their radii is 3:4, then, you have:
r1/r2 = 3/4
Take into account that the surface area of a cone is given by the following formula:
S = πrs + πr²
where s is the slant height of the cone. The first term is the area of the base and the second term the area of teh rest of the cone. Due to the cones are similar, then, the ratio of their slant height is
s1/s2 = 3/4
b) The ratio of their volumes is:
V1 = 1/3 ·π·r1²·h1
V2 = 1/3 ·π·r2²·h2
V1/V2 = (1/3 ·π·r1²·h1)/(1/3 ·π·r2²·h2)
V1/V2 = (r1/r2)²(h1/h2)
h1/h2 = 3/4, then:
V1/V2 = (3/4)²(3/4) = (3/4)³ = 27/64