A cone has a radius of 15 cm and a volume of 540 cm^3. what is the volume of a similar cone with a radius of 10 cm?

160 cubic centimeters

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

Let

z ---> the scale factor

----> the ratio of corresponding radii

simplify

step 2

Find the volume of the smaller cone

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z ---> the scale factor

x ----> the volume of the smaller cone

y ---> the volume of the larger cone

we have

substitute

5x+40

5(x + 8)

7x - 49

7(x - 7)

18x + 9

9(2x + 1)

15x - 10

5(3x - 2)

step-by-step explanation:

for number one all you have to do is factor 5 out of 5x + 40

for number 2 factor 7 out of 7x - 49

for number three factor 9 out of 18x + 9

for number four factor 5 out of 15x - 10

answer: when you burn wood, the carbon reacts with the oxygen in the air to create ash and smoke. that is a permanent change you cannot undo that.

step-by-step explanation: