what is the volume of helium required to fill a spherical balloon so that its surface area is 1200cm2(squared)
2007-06-15 06:08:29 · 7 answers · asked by Tina B 1 in Science & Mathematics ➔ Mathematics
4pir^2 = 1200
r^2 = 1200/4pi = 300/pi
V= 4/3 pir^3
V = 4/3 pi(300/pi)(sqrt(300/pi)
V= (400)sqrt(300/pi)
V approx = 3908.82 cm^3
2007-06-15 06:19:37 · answer #1 · answered by ironduke8159 7 · 0⤊ 0⤋
The surface area of a sphere is 4 pi r^2. Set this equal to 1200 and solve for r. Now that you have the radius, use this to get the volume using the formula for a sphere's volume:
(4/3)pi r^3
2007-06-15 06:13:13 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Homework!!
Set 4pi*r^2=1200, solve for r, then compute V=(4/3)pi*r^3.
2007-06-15 06:12:03 · answer #3 · answered by mathematician 7 · 0⤊ 0⤋
The formula of surface area is 4pi*r^2.
So, 1200=4pi*r^2.
So, r^2=1200/(4*pi).
So, r=sqr(300/pi).
And formula of volume is (4/3)pi*r^3.
So, volume is (4/3)pi*(sqr(300/pi))^3 = 3908.82 approximately.
(Check my calculations for errors though!)
2007-06-15 06:20:50 · answer #4 · answered by yljacktt 5 · 0⤊ 0⤋
1200= 4 pir^2 (formula of surface area
sq rt (1200/4*pi) = r = 9.7720502380
Volume = 4/3 *pi* r^3 = 3909 cubic centimeter
2007-06-15 06:21:52 · answer #5 · answered by kkr 3 · 0⤊ 2⤋
volume of a sphere = V = 4/3 * pi * r^3
area of a sphere = A = 4 * pi * r^2
so r = (A/(4*pi))^.5
substituting gives
V = 4/3 * pi * [(A/(4*pi))^.5] ^3 = 1/6 * pi * [(A/(pi))^.5] ^3
V =1/6 * (1/pi)^.5 * A^(1.5) = 1/6 *(1/pi)^.5 * (1200cm^2)^(1.5)
= 3909 cm^3
2007-06-15 06:25:12 · answer #6 · answered by Dr W 7 · 0⤊ 0⤋
Ok, find the radius first:
SurfArea = 4(Pi)r^2, so r = sqrt(Surf/Pi/4) = 9.772 cm.
Volume = (4/3)(Pi)r^3 = 3908.8 or 3900 cm3 (cubed)
2007-06-15 06:14:20 · answer #7 · answered by anotherhumanmale 5 · 0⤊ 0⤋