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3 years ago

A cone with volume 1350 m³ is dilated by a scale factor of 1/3.

Mathematics

2 answers:

faltersainse [42]3 years ago

8 0

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

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

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

$V=\dfrac{1}{3}\pi r^2h=1350\\\\\\\Rightarrow \pi r^2h=4050.$

Now, if we dilate the cone by a scale factor of $\dfrac{1}{3}$ , then the radius and height will become one-third of the original one.

Therefore, the volume of the dilated cone will be

$V_d=\dfrac{1}{3}\pi (\dfrac{r}{3})^2\dfrac{h}{3}=\dfrac{1}{81}\times \pi r^2h=\dfrac{1}{81}\times 4050=50.$

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

ki77a [65]3 years ago

6 0

Answer:

450

Step-by-step explanation:

You basically do 1350 * 1/3 or 1350/3

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