Question

A cone with volume 2880 m³ is dilated by a scale factor of 14.

What is the volume of the resulting cone?

Answer 1

A scale factor is the ratio of two similar geometric figures of their corresponding sides. The scale factor is calculated by locating the corresponding sides on each figure. We calculate as follows:

volume of the resulting cone = 2880 x 14 = 40320 m^3

Hope this answers the question. Have a nice day.

Answer 2

`45m^3`

Explanation:

Volume of cone = 2880 m³

Since the cone is dilated by scale factor of
`(1)/(4)`

So, the dimensions will become one-fourth of the previous dimensions

Volume of cone :
`2880=(1)/(3) \pi * r^(2) * h` -a

After the dilation by scale factor
`(1)/(4)`

`r\rightarrow (r)/(4)`

`h\rightarrow (h)/(4)`

So,
`(1)/(3) \pi *(r)/(4)^(2) *(h)/(4)`

`(1)/(3) \pi *(r^2)/(16)* (h)/(4)`

`(1)/(64) * (1)/(3) \pi *r^2* h`

So, the original volume becomes
`(1)/(64)`

Using a

`(1)/(64) *2880`

`45m^3`

Hence the volume of the resulting cone is
`45m^3`