i need help with a problem, if not fully explained then i might need help with another problem.
I was given the formula for the volume of a sphere i, but i still don't know what to do. if you could explain to me thatll be great. Tanks
The radius of a spherical balloon is 1/2 foot. The radius of a second one is 3/4 foot. How do the volumes of the balloons compare?
Tank you tutors
r1 = radius of a larger sphere
r2 = radius of a smaller sphere
Volume of a sphere is given by the formula :
V = ( 4 / 3 ) pi * r ^ 3
Vollume of a larger sphere :
V1 = ( 4 / 3 ) pi * r1 ^ 3 =
( 4 / 3 ) pi * ( 3 / 4 ) ^ 3 =
Vollume of a smaller sphere :
V2 = ( 4 / 3 ) pi * r2 ^ 3 =
( 4 / 3 ) pi * ( 1 / 2 ) ^ 3 =
V2 / V1 = [ ( 4 / 3 ) pi * ( 3 / 4 ) ^ 3 ] / [ ( 4 / 3 ) pi * ( 1 / 2 ) ^ 3 ] =
( 3 / 4 ) ^ 3 / ( 1 / 2 ) ^ 3 =
[ ( 3 / 4 ) / ( 1 / 2 ) ] ^ 3 =
[ ( 3 * 2 ) / ( 4 * 1 ) ] ^ 3 =
( 6 / 4 ) ^ 3 =
[ 3 * 2 / ( 2 * 2 ) ] ^ 3 =
( 3 / 2 ) ^ 3 =
3 ^ 3 / 2 ^ 3 =
27 / 8 = 3.375
This mean :
The ratio of the volumes of spheres is proportinal to cube of its radius.
V1 / V2 = ( r1 / r2 ) ^ 3
In this case :
V1 / V2 = ( r1 / r2 ) ^ 3 = ( 0.75 / 0.5 ) ^ 3 = 1.5 ^ 3 = 3.375