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=(diameter)/(2)\\ d=diameter\\ ----------\\ d=5.7\\ r=(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`