Question 1105414
<br>
The total surface area of a cone is the lateral surface area plus the area of the base:
{{{A = (pi)(r)(l) + (pi)(r^2)}}}<br>
If the radius of the cone is tripled and the slant height is cut by a factor of 3, the lateral surface area stays the same:
{{{(pi)(3r)(l/3) = (pi)(r)(l)}}}<br>
The area of the base changes; it is now
{{{(pi)(3r)^2 = 9(pi)(r^2)}}}<br>
The lateral surface area stays the same; the area of the base increases by {{{8(pi)(r^2)}}}; so the total surface area of the cone increases by {{{8(pi)(r^2)}}}.