If the radius of a sphericallyshapedsphere is doubled the volume is...???

Question

Im stuck...

Answer 1

Lengths are linear
So a line that doubles will increase its length by 2.

Areas are squared
So a circle that doubles radius will increase its area by 4.

Volumes are cubed
So a sphere that doubles radius will increase its volume by 8.

You can get into the specifics of the formulas for circles and spheres, but basically you just need to notice that in an area formula you have r², so if you have (2r)² it's the same as 4r². Similarly in a sphere you have an r^3 term, and putting in (2r)^3, you have the same as 8r^3.

It doesn't matter if it is a cube, a sphere, a pyramid or some other 3-D shape. If the dimensions are doubled for all three dimensions (length, width, height) then the volume increases by a factor of 2^3 or 8.

The answer to your question is:
"...the volume is multiplied by 8."

P.S. Technically, just like the words for doubled and quadrupled, you could say "octupled". The dictionary defines this as "to multiply or be multiplied by 8".

Answer 2

The formula for a sphere's volume is pi, times the cube of the radius.

So, if the radius of a sphere is 2 feet, the formula works as:

pi, times 2 cubed (2 times 2 times 2 = 8)

If the radius is doubled to 4 feet, the formula works as:

pi times 4 cubed (4 times 4 times 4 = 64)

I'll let you do the math, because I don't know to how many decimal places you must figure on pi.

Answer 3

radius is linear. Volume is cubic. There fore volume varies as r^3
if you double the radius is doubled, volume is 8 times as much.

Answer 4

Is this a riddle--a sphere is supposed to be spherically-shaped right? I'm really not getting this question.

Answer 5

8, whether the spherically-shaped sphere is spherical, round or orb-shaped.

Answer 6

multiplied by eight.
V= 4π(r^3)/3, so if r=2r, V=4π[(2r)^3]/3=4π8(r^3)/3