Aright circular cylinder is placed in the center of a cube shaped container as shown in the figure below. each edge of the interior container measures 6inches. the diameter of the base of the cylinder is 4inches and the height is 6inches. a liquid will be poured around the cylinder completely fill the container to create a mold. which of the following values is closest, in cubic inches, to the total value that will be needed to create the mold?

Given:

A liquid will be poured around the cylinder completely fill the container to create a mold. Illustrated in the figure is a cylinder inside a cube. The cube's sides are all 6 inches. The cylinder has a diameter of 4 inches and a height of 6 inches. 

The total volume of the mold is determined by:

Volume of mold = Volume of the cube - volume of the cylinder
                            = s^3 - pi*r^2*h
                            = 6^3 - 3.1415*2^2*6
                            = 140.604 cubic inches
Therefore, the volume of the liquid needed to create the mold is 140.60 cubic inches. 

First step is to get rid of the square root. remember that a square root is the same as raising to the (1/2) power. see below: multiply exponents per exponent rules to get: remember you subtract exponents from the denominator and add exponents in the numerator so: simplify further: so a is the correct choice. if you don't understand this google exponent rules and it will you understand. look at the image results.