Rachel is frosting the top of two cakes and wants to know which cake will require more frosting. one cake is round with a diameter of 8 inches. the other cake is square with a length of 9 inches. the top of which cake has a larger area? how much larger is it? fast i need this you

The square cake is larger by 31 in^2

Step-by-step explanation:

A round cake has a circular area on top.

We need to find the radius

d= 2r

8 = 2r

r=4

The area of the circle is pi r^2

A = 3.14 * 4^2

A = 3.14 *16

   = 50.24

The area of the square cake is

A =s^2

A = 9^2

A = 81

The square cake is larger

The difference is Asquare - A round

81 -50.24

30.76

Which is close to 31 in ^2

1. write each boy's age in terms of x
Here's what we can do to represent each boy's age in terms of x:

1st brother = x + 2 (he is two years older than than 3nd brother)
2nd brother = x + 1 (he is one year older than 3rd brother)
3rd brother = x   (he is the youngest so we use x to represent him)

2. Write an equation to represent the situation:

1st brother's age times 3rd brother's age equals 20 more than twice 2nd brother's age

(1st brother's age)*(3rd brother's age) = 20 + 2(2nd brother's age) 

(x+2)*(x) = 20 + 2(x+1)

3. Now we need to solve for x.

(x+2)(x) = 20 + 2x +2
Foil the stuff in the parentheses

x^2 + 2x = 20 + 2x +2
Move everything to the same side

x^2 + 2x - 20 - 2x -2 = 20 + 2x +2  - 20 - 2x -2
all that crazy stuff becomes: x^2 - 22  = 0
Solve the polynomial

x^2 - 22 = 0
remember a^2 - b is the same as (a+√b)(a-√b) 
so x^2 - 22 = (x+√22)(x-√22)

This means (x+√22)(x-√22) = 0
so x = √22 or -√22

Age obviously won't be negative so x = √22 in this case. 
By the way: √22 also equals 4.69

4. Find out how old the three brothers are.

x = 3rd brother's age
x + 1 = 2nd brother's age
x + 2 = 1st brother's age
substitute √22 or 4.69 for x.

3rd brother = 4.69 years old (or √22 years old to be more precise)
2nd brother = 5.69 years old (or √22 + 1)
1st brother = 6.69 years old (or √22 +2)

Important NOTE: I think you made a mistake in typing the question. It might have been "consecutive even integers" rather than what you typed which was "consecutive integers". If the question contained "consecutive even integers"  than the brother's ages would have been 4, 6, and 8 instead of some funky decimal numbers.

Hope this answered your question, but if it was too confusing feel free to ask any questions you have.