A basketball has a surface area of 1810 in^2 and a baseball has a surface area of 6 in^2.
What is the diameter of a baseball if the diameter of a basketball is 9.5 in^2.
area is proportional to length dimension squared for similar objects
D^2/d^2 = A/a
Howevr what you typed makes no sense.
1. diameter of basketball is not in square inches
If the diameter is 9.5 inches, the area is not 1810
area = 4 pi r^2 =4*3.14*4.75^2 =283 in^2
by the way volume =(4/3) pi r^3 =448 in^3
1. A diameter has a diameter measured in inches not inches^2
2. A basketball with a diameter of 9.5 inches has a radius of 4.75 inches and a surface area of
4π(4.75)^2 in^2 or 283.53 in^2 , not 1810
But all that is not needed
if the radius of the baseball is r inches, then
4πr^2 = 6
r^2 = 3π/2
r = appr 2.1 inches, so the diameter would be 4.2 inches according to the given data
To find the diameter of a baseball, we can use the fact that the surface area of a sphere is directly proportional to the square of its diameter.
First, let's find the ratio of the surface areas of the basketball and the baseball:
Surface area of basketball / Surface area of baseball = 1810 in² / 6 in² = 301.67
Since the surface areas are proportional to the square of the diameters, we can set up the following equation:
(Diameter of basketball)² / (Diameter of baseball)² = 301.67
Now we can solve for the diameter of the baseball. Rearranging the equation, we have:
(Diameter of basketball)² = (Diameter of baseball)² * 301.67
We know the diameter of the basketball is 9.5 inches, so we can substitute the values:
(9.5 in)² = (Diameter of baseball)² * 301.67
Simplifying, we get:
90.25 = (Diameter of baseball)² * 301.67
Dividing both sides of the equation by 301.67, we have:
(Diameter of baseball)² = 90.25 / 301.67
Taking the square root of both sides, we find:
Diameter of baseball ≈ √(90.25 / 301.67)
Calculating this on a calculator, we get:
Diameter of baseball ≈ 2.47 inches
Therefore, the diameter of the baseball is approximately 2.47 inches.