Answer:
[tex]15\pi[/tex] sq. cm.
Step-by-step explanation:
The lateral area of a cone is given by the formula [tex]\pi rl[/tex]
Where, r is the radius, and l is the slant height
r is given as 3 cm, but slant height is not given. Let's use the pythagorean theorem on the triangle created by 3cm , 4cm, side and lateral side (slant height).
Let slant height be l:
[tex]3^2+4^2=l^2\\25=l^2\\l=5[/tex]
Now plugging into the formula, we get:
Lateral area = [tex]\pi rl = \pi (3)(5)=15\pi[/tex]
Second answer choice is right, [tex]15\pi[/tex] sq. cm
