The volume, V, of a sphere is given as a function of its radius, r, by
V = 4/3πr^2
Write V as proportional to a power of r. What is the constant of proportionality?
I do not understand!! Please help explain this problem so i can do my homework... is the constant 4/3π??
2006-09-14 12:23:53 · 8 answers · asked by ellenangel364 3 in Science & Mathematics ➔ Mathematics
π is supposed to be pi
2006-09-14 12:24:15 · update #1
Writing V as proportional to a power of r means to write it as:
V= c * r^n where c is the constant of proportionality and n is the power.
Your answer: 4/3 times pi is right. assuming you meant to type that and not 4/(3pi).
2006-09-14 12:30:38 · answer #1 · answered by Demiurge42 7 · 1⤊ 0⤋
Volume is never proportional to r^2 (why?)
any physicist here?
for those ignorant in mathematics:
sphere, in geometry, the three-dimensional analogue of a circle. The term is applied to the spherical surface, every point of which is the same distance (the radius) from a certain fixed point (the center), and also to the volume enclosed by such a surface. The curve formed by a plane cutting a sphere is a circle. If the plane goes through the center of the sphere, the circle is called a great circle of the sphere. It is the largest circle that can be drawn upon the sphere, and all great circles of the same or equal spheres are of equal size. The shortest distance between two points on a spherical surface, measured on the surface, is the distance along the great circle through those points. A plane cutting a sphere in a great circle divides the sphere into two equal segments called hemispheres. The diameter of a sphere is the diameter of one of its great circles. The formula for the area of the surface of a sphere is S=4πr2, and for the volume it is V=4⁄3 πr3, where r is the radius of the sphere. Spherical geometry and spherical trigonometry are methods of determining magnitudes and figures on a spherical surface.
2006-09-14 12:34:43 · answer #2 · answered by oracle 5 · 0⤊ 1⤋
Two quantities are called proportional if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio.
V = 4/3(pi)r^2 = kr^2 where k = constant of proportionality = 4/3(pi)
2006-09-14 12:29:13 · answer #3 · answered by williegod 6 · 1⤊ 0⤋
4/3π is a constant, so I'd say "yes"
2006-09-14 12:29:36 · answer #4 · answered by Anonymous · 0⤊ 1⤋
it might be 4/3 pi (dont know how u do that thing) r..it think so!!
2006-09-14 12:28:33 · answer #5 · answered by desire_4_life_4_shoo 1 · 0⤊ 1⤋
Yep that seems correct
2006-09-14 12:45:26 · answer #6 · answered by Cutecici 1 · 0⤊ 1⤋
You are correct!
2006-09-14 12:32:32 · answer #7 · answered by MollyMAM 6 · 0⤊ 1⤋
I KNOW NOTHING JUST NEED THE POINTS!
2006-09-14 12:27:07 · answer #8 · answered by money lover 2 · 0⤊ 2⤋