where's the diagram? is the distance between a and b the length of the entire cone? as in 12cm?
The right circular cone in the figure below is intersected halfway between point (A) and point (B) by a plane parallel to the base of the cone. The height of the cone is 12 centimeters (cm) and the radius of the base is 5 centimeters.
A smaller cone is created by the intersection of the cone and the plane. Which is closest to the area of the base of the smaller cone?
A. 7.9 square centimeters
B. 15.7 square centimeters
C. 19.6 square centimeters
D. 39.3 square centimeters
Okay, i assume the distance between point a and b is the entire length of the cone, so then the plane cuts the cone 6 cm from the top. Sorry, but i'm on a school pc with no paint or anything and cant draw a diagram for you. but if you take a cross section of the cone (which will look like a triangle) and draw a line through the cone parallel to the base of the cone, you will realize you obtain similar triangles. Cut this triangle into two right angled triangles (with a line perpendicular to the base to the vertex of the cone). Now since these are similar triangles, the base/height ratio of one is equal to the base/height ratio of the other.
Let r be the radius of the new cone.
Then r/6 = 5/12 => r = 5/2
Now the hard part is done, we just plug in this new value for r into the formula for the area of a circle.
A = pi*r^2
=> A = pi*(5/2)^2
A = 25pi/4 = 19.6 square cm
So choice C is the answer (provided i had the distance between a and b correct)
I added a sketch below