Can anybody help me with finding the radius of a sphere!?

Question

I have a sphere that weighs 56.7 grams. Also, I know that the sphere has a density of 11.352 grams per cubic centimetre.

Is it possible for me to find the radius of the sphere. I was thinking of perhaps trying to use the sphere volume formula which is:

4/3 * pi * radius cubed

Perhaps I could get the radius isolated but I'm kinda struggling. Is it possible to find the radius using only the mass and density? I know the answer is like 21.208 or something but I don't know how to get it.

Please help! Any answers or help are appreciated. Thankyou!

By the way, this has something to do with shotgun bores and gauges. Using some formula I found on wikipedia, the answer seemed to be 21.208mm. However, I can't seem to get that answer...

Answer 1

Well, density = mass/volume, so volume = mass/density. To three significant figures, that's 4.99 cm^3.

Now take V = (4/3)(pi)(r^3) and solve for r.

(3/4)V = (pi)(r^3)

r^3 = (3V)/(4pi)

So r = the cube root of [(3V)/(4pi)], which is (again, to 3 SF) 1.06 cm.

Your "Wikipedia answer" (~21.2 mm) would be the diameter of the sphere, not the radius. 21.2 mm = 2.12 cm = 2 * 1.06 cm.

Answer 2

Radius Of A Sphere

Answer 3

yeah, you know it dude.. you're just confused...

you can get volume from the given density and mass;

density = mass / volume

so

volume = mass / density
volume = 56.7 / 11.352
.............= 4.9947 cubic cm.

Use this volume to compute for the radius, knowing that

volume(V)= 4/3 * pi * r^3

by formula transformation, you'll come up with a formula for radius (r) as:

r = cube root of (3/4 * V / pi)
r = cube root of (3/4 * 4.9947 / pi)
r = **solve on, use your calculator to get the final answer

Answer 4

Density is equal to mass divided by the volume, i.e.,

D=m/v

So we can find the volume of the sphere by making volume the subject of the formula;
v=m/D
v= 56.7/11.352
v= 4.99 cubic centimetres ( 2 decimal places)

So the radius of the sphere is
v= 4/3 * pi * radius cubed
4.99= 4/3 * pi * radius cubed
solve for radius and the answer comes to 1.09 cm.

Answer 5

You're on the right track. The missing piece is how you get the volume from the mass and density.
Density is defined as mass / volume, so volume = mass / density = 56.7 / 11.352 = 4.995 cm^3.

Then we have V = (4/3) π r^3 to get the radius:
4.995 = (4/3) π r^3
<=> r^3 = (3/4) (4.995 ) / π = 1.192
so r = (1.192)^(1/3) = 1.06 cm.

Answer 6

You can use the formula that you quoted.

56.7/(4/3*(pi)*r^3) = 11.352
1/r^3 = (11.352*4*(pi))/(56.7*3) = 0.838645
r^3 = 1.1924
r = 1.0604 cm

Answer 7

The volume = 56.7/11.352 = 4.994
now 4/3*pi r^3 = 4.994

r^3 = 4.994 *3/(4*pi) = 1.19

r = (1.19)^(1/3) = 1.059 cm

Answer 8

nicely Ive been questioning in this ...and the only way i'd desire to do it it may be making use of water displacement? frinstance get a water-resistant field larger than the sphere, degree its quantity and fill it with water push the sphere under water and wait till the overflow stops, then re -degree the quantity of water in the sq. sided field??? the adaptation between finished and not finished would desire to be very very on the ingredient of the quantity of the sphere????

Answer 9

density=mass/volume
V=M/D = 4/3 R*R*R
R^3 = 3*56.7 / 4*3.14*113.52 = 1.1919
r= 1.0602cm