Two cones are given. The radius of the base and the generatrix of the first cone are 2 and 4, respectively

Two cones are given. The radius of the base and the generatrix of the first cone are 2 and 4, respectively, and that of the second, 6 and 8. How many times is the area of the lateral surface of the second cone and more than the area of the lateral surface of the first?

The lateral surface area of the cone is calculated by the formula:

S = Pi * r * l

where r is the radius of the base, l is the length of the generatrix of the cone.

At the first cone: r = 2, l = 4. Hence:

S1 = Pi * 2 * 4 = 8 * Pi.

At the second cone: r = 6, l = 8. Hence:

S2 = Pi * 6 * 8 = 48 * Pi.

We divide the area of the second cone by the area of the first to find out how many times it is larger:

S2 / S1 = 48 * Pi / 8 * Pi = 6.

Answer: 6 times.