The curved surface area of a frustum of a cone is \(\pi l(r_1+r_2)\), where \(l=\sqrt{h^2+(r_1+r_2)^2}\), \(r_1,r_2\) are radii and \(h\) is height.
Step 1: A frustum of a cone is formed when a small cone is cut off from a bigger cone by a plane parallel to its base.
Step 2: The formula for the curved surface area (CSA) of a frustum is:
\[ CSA = \pi l (r_1 + r_2) \]
where:
Step 3: The slant height \(l\) is found using Pythagoras theorem in the right-angled triangle formed by height \(h\), difference of radii \((r_1 - r_2)\), and slant height \(l\).
So,
\[ l = \sqrt{h^2 + (r_1 - r_2)^2} \]
Step 4: But in the given statement, \(l\) was written as:
\[ l = \sqrt{h^2 + (r_1 + r_2)^2} \]
This is wrong, because we must use the difference of radii \((r_1 - r_2)\), not the sum.
Step 5: Therefore, the statement is False.