Question

If the diameter of a sphere is doubled its surface becomes?

Answer 1

Surface area of a sphere: S=4pi%2Ar%5E2

Remember, the diameter is d=2r. So if the diameter is doubled, then the new radius is 2r units (instead of "r" units)


S=4pi%2Ar%5E2 Start with the given equation.


S=4pi%2A%282r%29%5E2 Replace the original "r" with "2r".


S=4pi%2A4r%5E2 Square 2r to get 4r%5E2



So the old equation is S%5Bold%5D=4pi%2Ar%5E2 and the new one is S%5Bnew%5D=4pi%2A4r%5E2


The ratio of the new surface area to the old surface area is then:

S%5Bnew%5D%2FS%5Bold%5D=%284pi%2A4r%5E2%29%2F%284pi%2Ar%5E2%29


Highlight the common terms


Cancel out the common terms


S%5Bnew%5D%2FS%5Bold%5D=4 Simplify

Answer 2

area will be four times the first area

Explanation:

the diameter of the first sphere=d

therefore radius=d/2

=r

the diameter of the second sphere becomes 2d

therefore the radius of second sphere=2r

area of a sphere=4×pi×r^2

the ratio of the two spheres=(4pi(2r)^2)/(4pir^2)

=(4pi4r^2)/4pir^2

cancelling 4pir^2, you get 4:1

therefore the area of the second sphere is 4 times the first one