Question

I need help!! (photo included)

Answer 1

a. The surface area is
`2828.25 cm^2`

b. The radius is 8 cm

Explanation:

The surface area of a beachball is modeled by the function

`f(x)=ax^2`

Where x is the radius of the beachball.

It's given that a beachball of radius 12 cm has a surface area of
`1809.56 cm^2`

This information will allow us to find the value of a by substituting in the model:

`1809.56=a*12^2=144a`

Dividing by 144:

a = 1809.56/144

a = 12.57

The model is now:

`f(x)=12.57x^2`

Now we can solve parts a and b:

a . Find the surface area of a beachball of radius x=15 cm

`f(15)=12.57*15^2`

`f(15)=2828.25`

The surface area is
`2828.25 cm^2`

b. Find the radius of a beachball with a surface area of
`804.25 cm^2`

We need to solve:

`804.25 = 12.57x^2`

Dividing by 12.57:

`x^2=804.25/12.57\approx 64`

Thus:

`x=√(64)`

x=8 cm

The radius is 8 cm