Answer:
a. The surface area is [tex]2828.25 cm^2[/tex]
b. The radius is 8 cm
Step-by-step explanation:
The surface area of a beachball is modeled by the function
[tex]f(x)=ax^2[/tex]
Where x is the radius of the beachball.
It's given that a beachball of radius 12 cm has a surface area of [tex]1809.56 cm^2[/tex]
This information will allow us to find the value of a by substituting in the model:
[tex]1809.56=a*12^2=144a[/tex]
Dividing by 144:
a = 1809.56/144
a = 12.57
The model is now:
[tex]f(x)=12.57x^2[/tex]
Now we can solve parts a and b:
a . Find the surface area of a beachball of radius x=15 cm
[tex]f(15)=12.57*15^2[/tex]
[tex]f(15)=2828.25[/tex]
The surface area is [tex]2828.25 cm^2[/tex]
b. Find the radius of a beachball with a surface area of [tex]804.25 cm^2[/tex]
We need to solve:
[tex]804.25 = 12.57x^2[/tex]
Dividing by 12.57:
[tex]x^2=804.25/12.57\approx 64[/tex]
Thus:
[tex]x=\sqrt{64}[/tex]
x=8 cm
The radius is 8 cm
