if the diameter of a spherical ball is doubled,by what factor does its surface area increase?
Isn't surface area proportional to the square of diameter?
yes but don't know wat surface area it increases
SA of sphere is 2pi(r)^2
so if you change the radius from r to 2r (or d to 2d)
then the SA is 2pi(2r)^2 = 8pir^2
so by what factor did it increase ?
To determine by what factor the surface area increases when the diameter of a spherical ball is doubled, we can use the formula for the surface area of a sphere.
The formula for the surface area of a sphere is given by:
A = 4πr²
Where A is the surface area and r is the radius of the sphere.
Since the diameter of a sphere is twice the radius, we can say that the radius is half the diameter:
r = d/2
If we double the diameter, the new diameter would be 2d. Substituting this value in the formula, we get the new surface area:
A' = 4π(2d/2)²
A' = 4π(d)²
A' = 4πd²
Dividing the new surface area by the original surface area, we get:
A' / A = (4πd²) / (4πr²)
Canceling out the common factors of 4π, we get:
A' / A = (d²) / (r²)
Since we know that r = d/2, we can substitute this value in the equation:
A' / A = (d²) / ((d/2)²)
A' / A = (d²) / (d²/4)
A' / A = 4
Therefore, when the diameter of a spherical ball is doubled, its surface area increases by a factor of 4.