What must be the radius of a sphere so that it's volume is equal to its surface area? Pls disregard the units of measurement.. so you won't be confused.
Thanks!
2007-08-16 01:27:48 · 5 answers · asked by double B 2 in Science & Mathematics ➔ Mathematics
Surface area = 4 pi r^2.
Volume = (4/3)pi*r^3.
So, 4 pi r^2 = (4/3)pi * r^3.
So, 3= radius..
2007-08-16 01:39:10 · answer #1 · answered by yljacktt 5 · 0⤊ 0⤋
area of sphere = 4*pi*r^3 / 3
surface area of sphere = 4*pi*r^2
Equate both :
4*pi*r^3 / 3 = 4*pi*r^2
4*pi*(r^3 - 3r^2) / 3 = 0
r^2( r - 3 ) = 0
r = 0 or 3
Notice that :
If r = 0, surface area = 0 and volume = 0
if r = 3, surface area = volume = 36*pi
2007-08-16 08:42:18 · answer #2 · answered by Maxis 2 · 0⤊ 0⤋
volume V= 4/3 *Pi *r^3
area A= 4*Pi*r^2
so
4/3 *Pi*r^3= 4*Pi*r^2
divide by 4*Pi*r^2 both sides
r/3=1 r=3
proof A= 4*Pi*9= 36*PI ; V =4/3*Pi*27=36*Pi
2007-08-16 08:37:10 · answer #3 · answered by maussy 7 · 0⤊ 0⤋
3
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2007-08-16 08:34:31 · answer #4 · answered by oregfiu 7 · 0⤊ 0⤋
(4/3)Ï r³=4Ï r²
(1/3)r=1
r=3
2007-08-16 08:38:46 · answer #5 · answered by ♫♪sree♪♫ 3 · 0⤊ 0⤋