Answer: The answer is 50 m³.
Step-by-step explanation: We are given to find the volume of the cone cone after being dilated by a factor of one-third from a cone with volume 1350 m³.
The volume of a cone with base radius 'r' units and height 'h' units is given by
[tex]V=\dfrac{1}{3}\pi r^2h.[/tex]
Therefore, if 'r' is the radius of the base of original cone and 'h' is the height, then we can write
[tex]V=\dfrac{1}{3}\pi r^2h=1350\\\\\\\Rightarrow \pi r^2h=4050.[/tex]
Now, if we dilate the cone by a scale factor of [tex]\dfrac{1}{3}[/tex], then the radius and height will become one-third of the original one.
Therefore, the volume of the dilated cone will be
[tex]V_d=\dfrac{1}{3}\pi (\dfrac{r}{3})^2\dfrac{h}{3}=\dfrac{1}{81}\times \pi r^2h=\dfrac{1}{81}\times 4050=50.[/tex]
Thus, the volume of the resulting cone will be 50 m³.
Answer:
50 m
Step-by-step explanation:
just took the test to prove it was the right answer:)
