This exercise could have been a piece o' cake, and fun in its own right,
if you had just told us what the "factor of ..." number is.
By whatever factor the radius increases, the volume increases by the cube
of that number.
The volume is increased by a factor of 23 = 8.
There is no equation for the "scale factor" of a sphere. If I assume you to mean how the volume increases with radius then you would use the volume equation for a sphere and calculate volume based on corresponding radii. You could then divide the resultant volumes to give a percentage or factor of how much larger or small one sphere is than another. You'll see that a small change in radius causes a large change in volume due to the volume being a cubic factor of the radius.
The volume increases by a factor of (3)3 = 27 times.
The volume of a sphere with a radius of 13 is: 9,203 units3
The volume of a sphere with a radius of 18 is about 24,429 units3
The volume is increased by a factor of 23 = 8.
64The formula to find the volume of a sphere is4/3 * pi * r3where r is the radius of the sphere. So if the radius is increased by a factor of 4, then the formula becomes4/3 * pi * (4r)3 = 4/3 * pi * 64r3showing that the volume increases by a factor of 64.
The volume of a sphere is proportional to R3 .So doubling the radius causes the volume to increase by a factor of 23 = 8 .
The radius must be increased by 26%. (rounded)
There is no equation for the "scale factor" of a sphere. If I assume you to mean how the volume increases with radius then you would use the volume equation for a sphere and calculate volume based on corresponding radii. You could then divide the resultant volumes to give a percentage or factor of how much larger or small one sphere is than another. You'll see that a small change in radius causes a large change in volume due to the volume being a cubic factor of the radius.
The volume of the sphere is proportional to the cube of its radius.Increasing the radius by 5% causes the volume to increase by the factor of (1.05)3= (1.05 x 1.05 x 1.05) = 1.157625= 15.7625% increase in volume.(Regardless of what the radius and volume were before the increase.)
The volume increases by a factor of (3)3 = 27 times.
The volume of a sphere with a radius of 4cm is about 268cm3
The volume of a sphere with a radius of 2cm is about 33.5cm3
The volume of a sphere with a radius of 13 is: 9,203 units3
The volume of a sphere with a radius of 18 is about 24,429 units3
A sphere with a radius of 9 units has a volume of 3,053.63 units3