Question

I need help!! (photo included)

Answer 1

Answer:

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

b. The radius is 8 cm

Step-by-step 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:

$x=\sqrt{64}$

x=8 cm

The radius is 8 cm