Question

If a polyhedron has a volume of 24cm^3 and is dilated by a factor of 4/5 what will be the volume of the dilated polyhedron? Round your answer to the nearest thousandth if necessary.

Help is appreciated! Medal to best answer! Thanks!

Answer 1

Hints:
1. When the dilation factor is less than one, it is actually a compression.
2. For a solid, the volume after dilation is equal to the original volume \(\times~(factor)^3\) .
3. Your calculator should help you get the correct answer, or post for checking.

Answer 2

Thanks. Can you help me set up the equation?

Answer 3

@mathmate

Answer 4

@phi

Answer 5

Equation is not required.
You just calculate directly the value.
For example,
A cube has volume 4\(m^3\), what is the volume after a dilation of 1.2
New volume = \(3(1.2)^3 m^3\)

Answer 6

so like, 24(4/5)^3 cm^3

Answer 7

@mathmate

Answer 8

exactly!

Answer 9

so 12.288 cm^3 is the answer?

Answer 10

Lemme check.

Answer 11

Yes, exactly!
\(\color{blue}{\Large\checkmark}{Way~to~go!}\)

Answer 12

THANKS SO MUCH! The question says to round to the nearest thousandth if necessary. So, do I leave it at 12.288 or do I make it 12.29?

Answer 13

12.288 is already to the nearest thousandth
(12.29 would be to the nearest 100th)

Answer 14

thanks phi

Answer 15

Can you help me with on more qestion?

Answer 16

if you post it.

Answer 17

Triangle A'B'C' is a dilation of triangle ABC. The scale factor is 1/4. Point B is 13 inches away from the center of dilation. How far away from the center of dilation is point B'? Write your answer as an improper fraction or a decimal. Distance from B' to the center of dilation = inches

Answer 18

ABC is the original. you multiply by the scale factor to get the new A'B'C'
in other words, you multiply the distance (from the center) by 1/4
what do you get ?

Answer 19

you get 3.25

Answer 20

yes

Answer 21

Is that the answer? or is there more?

Answer 22

@phi

Answer 23

that's the answer. 13/4 or 3.25

Answer 24

THANKS PHI!