Question

An automobile engineer is revising a design for a conical chamber that was originally specified to be 12 inches long with a circular base diameter of 5.7 inches. In the new design, the chamber is scaled by a factor of 1.5. What is the volume of the revised chamber? Round your answer to two decimal places.

Answer 1

$\bf \textit{volume of a con}\\\\ V=\cfrac{\pi r^2 h}{3}\qquad \begin{cases} h=height\\ r=radius=\frac{diameter}{2}\\ d=diameter\\ ----------\\ d=5.7\\ r=\frac{5.7}{2}=2.85\\ h=12 \end{cases}\implies V=\cfrac{\pi 2.85^2\cdot 12}{3}\\\\ -------------------------------$

$\bf \textit{now, that's the original, now, let's scale "r" and "h" by 1.5} \\\\\\ V=\cfrac{\pi r^2 h}{3}\qquad \begin{cases} r=2.85\cdot 1.5\\ h=12\cdot 1.5\\ ----------\\ r=4.275\\ h=18 \end{cases}\implies V=\cfrac{\pi \cdot 4.275^2\cdot 18}{3}$