Find the total area of three circles, each with a radious of 1 1/2 feet.

Let ii stand for pie

Te book gives the answer as 27ii/4
aprroimately 21.195

I know the equation and can calculate the 27.

A=ii (1)^2

A=ii (1.5)^2=3

3 X 3 circles =27ii

I am not clear where the 4 is coming from and why it would be 27ii/4?

The area of a circle is

A = pi*r^2 OR
A = pi*(D/2)^2 = (pi*D^2)/4
That's where the 4 comes from.
Note that the spelling of the Greek letter pi.

I don't think I am understanding correctly?

Was I also suppose be using d=2r?

the radius, is 1.5 ft = 3/2 ft

then the radius squared is 9/4
then
pi r^2 = pi (9/4)
then three of those is pi (27/4)

To find the total area of the three circles, we need to calculate the individual area of one circle and then multiply it by 3. The equation to find the area of a circle is:

A = πr²

Given that the radius of each circle is 1 1/2 feet, we can substitute this value into the equation:

A = π(1.5)²

Simplifying further, we get:

A = π(2.25)

Now, we can calculate the individual area of one circle:

A = 2.25π

Since we have three circles, we need to multiply the individual area by 3:

Total Area = 3(2.25π)

Now let's simplify further:

Total Area = 6.75π

However, the book provides the answer as 27π/4. To understand why, we need to rationalize the denominator.

To rationalize the denominator, we multiply the numerator and denominator by 4:

Total Area = (6.75π * 4) / 4

Now, simplify the numerator:

Total Area = 27π / 4

So, the book's answer of 27π/4 is equivalent to 6.75π.

As for the approximate value of 21.195, that seems to be a rounding off error. The exact value for the total area is 27π/4.