The volume of the frustum of a cone is \(\dfrac{1}{3}\pi h[r_1^2+r_2^2-r_1r_2]\), where \(h\) is vertical height of the frustum and \(r_1, r_2\) are the radii of the ends.
Step 1: Recall the correct formula for the volume of a frustum of a cone.
It is: \(V = \dfrac{1}{3}\pi h (r_1^2 + r_2^2 + r_1r_2)\)
Step 2: Compare the given formula with the correct one.
Given: \(\dfrac{1}{3}\pi h(r_1^2 + r_2^2 - r_1r_2)\)
Correct: \(\dfrac{1}{3}\pi h(r_1^2 + r_2^2 + r_1r_2)\)
Step 3: Notice the difference.
The given formula has a minus sign (\(-r_1r_2\)) instead of a plus sign (\(+r_1r_2\)).
Step 4: Therefore, the statement is wrong.
Final Answer: False