# Thread: Area of a frustum

1. ## Area of a frustum

I know that $A=\pi (R+r)\sqrt{(R-r)^2+h^2}$

Question: Two mathematically similar frustums have heights of 20 and 30cm. The surface area of the smaller frustum is 450cm^2.

Calculate the surfce area of the larger frustum

My workings:
$450=(\pi R+r)^2\cdot (R-r)^2+400$

$50=(\pi (R+r))^2(R-r)^2$

2. ## An alternative method

I'll assume your formula for the surface area of the frustum is correct. However you can find the surface area sought in this problem without the formula.

The surface area of an object is proportional to the square of the characteristic dimension of the object. For instance, the surface area of a cube is 6*s^2 -> note the s^2 part.

Since your 2 objects are similar, and we know the surface area of the smaller object is 450 with characteristic dimension 20, we know the proportionality constant is k = 450/(20^2).

Now we calculate the surface area of the larger to be
A = k * 30^2 = (9/4) * 450 = 1012.5