Question

30 POINTS!!!!! (answer with work please)

1) A cone with volume 1350 m³ is dilated by a scale factor of 1/3. What is the volume of the resulting cone?

2) The top of the silo is a hemisphere with a radius of 11 ft. The bottom of the silo is a cylinder with a height of 38 ft. How many cubic feet of grain can the silo hold? Use 3.14 for pi and round your answer to the nearest cubic foot.

Answer 1

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

$V=\frac{1}{3}\pi r^2h.$

Therefore, if 'r' is the radius of the base of original cone and 'h' is the height, then we can write

$V=\frac{1}{3}\pi r^2h=1350$

⇒ $\pi r^2h=4050.$

Now, if we dilate the cone by a scale factor of , then the radius and height will become one-third of the original one.

Therefore, the volume of the dilated cone will be

$V_d=\frac{1}{3}\pi (\frac{r}{3})^2\frac{h}{3} =\frac{1}{81}$ × $\pi r^2h=\frac{1}{81}$ × $4050=50$

Thus, the volume of the resulting cone will be 50 m³.