If I have a marble that measures 15mm across how do I make it 10 x bigger?

Question

If I have a marble that measures 15mm across how do I make it 10 x bigger?

Answer 1

If you're talking volume, then the volume of a sphere is (4pi r^3)/3. As the diameter is 15mm, the radius must be 7.5mm.

It can therefore be written that (4pi*7.5^3)/3= 1767.14 (with the units being mm^3).

However, we want ten times that volume, so to express the new volume, we can write:

(4pi*r^3)/3=17671.4 (which is ten times the original volume).

We can now rearrange it to show the new radius.

4pi*r^3=16875pi

r^3=16875pi/4pi

r^3=4218.75

r= cubed root 4218.75

r=16.158...

So the radius of the larger sphere must be 16.158mm, and the diameter must be 32.31 mm.

Hope that helps, though I'm guessing it seems annoyingly complex.

Answer 2

A marble is spherical, and thus has a volume defined by

V = (4/3)π (r^3)

where V is volume and r is radius

so the diameter (2r) is 15 mm and therefore r = 7.5 mm

V = (4/3)π (7.5)^3 = 562.5 π mm^3

so a volume ten times larger would be 5625 π mm^3

the radius would then be:

r^3 = (3/(4π))(5625π)

r = 16.16 mm

2r = 32.32 mm

therefore, increase diameter by 17.32 mm to 32.32 mm across

Answer 3

You get a 15cm marble.

Answer 4

Look at it using a magnifying glass with a magnitude of, erm, 10.