Find the volume of the solid whose base is the region Ix I Iy I < 1 and whose vertical cross sections perpendicular to the y-axis are semicir- cles (with diameter along the base) g

volume of the solid =

Step-by-step explanation:

As given , the region : |x| + |y| 1

when y 0 ,

|x| + y = 1

⇒|x| = 1 - y

when y ≤ 0 ,

|x| - y = 1

⇒|x| = 1 + y

The given region is the rectangle with sides (0, 5) , (0, -5), (5, 0), (-5, 0)

As given , the vertical cross section are semicircle

As we know that the area of semi circle  =

Now,

Volume = +

            = -

           = [1-0] - [0-1]

           =

⇒volume of the solid =

Ratio = Cleaner : Water
                   1     :    3


Find total parts :

Total parts = 1 + 3 = 4


Find 1 part :

4 parts = 1 gallon
1 part = 1/4 gallon


Find 3 parts :

1 part = 1/4 gallon
3 parts = 1/4 x 3
3 parts = 3/4 gallon

Ratio = Cleaner : Water
                   1     :    3
                  1/4   :  3/4


You will need 1/4 gallon of cleaning solution.