A hollow sphere has outer radius 300 mm & thickness is 50 mm. If from this hollow sphere, we make a solid sphere then what is it's diameter=?
2006-10-03 20:21:22 · 9 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
450 mm ( approx)
2006-10-03 22:19:22 · answer #1 · answered by Anonymous · 0⤊ 1⤋
449.5568
I'm not sure I understand what you mean by making a solid sphere from the holw sphere. assuming you mean taking that amount of metal and melting it down into a solid sphere (because just filling it up into a solid sphere would be too easy), here's how I'd do it:
the volume of a sphere is V = (4/3)r^3*pi. with a radius 300, that's (4/3)*pi*2.7*10^7 for the entire sphere. the hollow part has a radius of 250, so the volume of the hole is (4/3)*pi*1.5625*10^7.
the volume of just the metal would be the total volume minus the empty volume, or (4/3)*pi*1.1357*10^7.
now take that volume and use it as the total volume for a solid sphere. V = (4/3)*pi*1.1357*10^7 = (4/3)*pi*r^3. to find the radius of the new sphere, 1.1357*10^7 = r^3.
take the cube root, 224.7784 = r
so 449.5568 mm = diameter
2006-10-04 03:41:08 · answer #2 · answered by Emily 3 · 0⤊ 0⤋
V = 4/3pi(R^3 - r^3) (where R = outer radius and r = inner radius of hollow sphere)
= 4/3 pi (300^3 - 250^3)
= 4/3 pi RS^3 (where RS = radius of solid sphere)
Thus RS^3 = 300^3 - 250^3
= 27000000 - 15625000
= 11375000
Thus RS = (11375000)^(1/3)
= 224.897 mm (approx)
Whence its diameter = 2*RS
= 449.794 mm
2006-10-04 03:34:33 · answer #3 · answered by Wal C 6 · 0⤊ 0⤋
Volume of a sphere is (4pi/3) r^3.
The material in the first sphere has a volume V1 of (4pi/3) (r_o^3-r_i^3), where r_o and r_i are the outer and inner radii.
Put V1 equal to (4pi/3) R^3, where R is the radius of the solid sphere.
This leads to R^3 = r_o^3-r_i^3. Plug in the values of 300 and 250 for the outer and inner radius. Then R= 225 mm (rounded of to mm).
Therefore the diameter is 450 mm.
2006-10-04 03:34:51 · answer #4 · answered by cordefr 7 · 0⤊ 0⤋
the volume of material used in hollow sphere:
volume using outer radius - volume using inner radius (or outer radius - thickness)
find the diameter of the solid sphere if the volume is the same as the material used above.
2006-10-04 03:26:28 · answer #5 · answered by Anonymous · 0⤊ 0⤋
Radius= 300, Thickness= 50,Volume= 3.14(300*300*300)- 3.14(250*250*250) = 3.14*11375000
If this volume is made into solid sphere,
(Radius) cube = 3.14*11375000/ 3.14
Radius= Approx.225 mm
2006-10-04 04:19:39 · answer #6 · answered by SGraja 4 · 0⤊ 0⤋
Either I'm crazy or you all are. Hollow/solid/sphere or circle, diameter is always 2r.
2006-10-04 03:31:28 · answer #7 · answered by vinny_the_hack 5 · 0⤊ 0⤋
V=pi(Ro^3-Ri^3) = pir^3
r = (Ro^3-Ri^3)^(1/3)
r = 50*(6^3-5^3)^(1/3)
r = 224.897 mm
d = 449.794 mm
2006-10-04 03:44:57 · answer #8 · answered by Helmut 7 · 0⤊ 0⤋
500mm
2006-10-04 03:23:24 · answer #9 · answered by Tony_Dimo 1 · 0⤊ 0⤋