both the diameter and height of a cylindrical vase are 2.5 times greater than a similar vase. the surface area of the smaller vase is 2826 square centimeters. whats is the surface area of the larger vase?

17662.5 cm2

Step-by-step explanation:

The surface area of a cylinder is given by the following formula:

Surface area = (pi*d^2) / 4 + pi*d*h

Where d is the base diameter and h is the height.

Is the diameter and the height are 2.5 times greater, we have that the new surface area is:

New area = pi * (2.5d) ^2/4 + pi*2.5d*2.5h = 6.25*pi*d^2/4 + 6.25*pi*d*h = 6.25 * (Surface area)

So the larger vase have a area of 6.25 * 2826 = 17662.5 cm2