Write 'True' or 'False' and justify your answer:
The volume of the frustum of a cone is $\frac{1}{3} \pi h[r_{1}^{2} + r_{2}^{2}-r_{1} r_{2}],$ where $h$ is the vertical height of the frustum and $r_{1}, r_{2}$ are the radii of the ends.
The volume of the frustum of a cone is $\frac{1}{3} \pi h[r_{1}^{2} + r_{2}^{2}-r_{1} r_{2}],$ where $h$ is the vertical height of the frustum and $r_{1}, r_{2}$ are the radii of the ends.
(B) False.
The correct formula for the volume of the frustum of a cone is $V = \frac{1}{3} \pi h(r_{1}^{2} + r_{2}^{2} + r_{1}r_{2}),$ where $h$ is the vertical height of the frustum and $r_{1}, r_{2}$ are the radii of the circular ends. The given expression contains a negative sign instead of a positive sign for the term $r_{1}r_{2}$.
The correct formula for the volume of the frustum of a cone is $V = \frac{1}{3} \pi h(r_{1}^{2} + r_{2}^{2} + r_{1}r_{2}),$ where $h$ is the vertical height of the frustum and $r_{1}, r_{2}$ are the radii of the circular ends. The given expression contains a negative sign instead of a positive sign for the term $r_{1}r_{2}$.
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