A.) The formula for the volume of a sphere is given below and the relationship between the radius r and the diameter d is r=d/2. Find the EXACT volume of the sphere in terms of the diameter d. Be sure to fully simplify the expression. B.) What is the EXACT volume of the sphere when the diameter is 2/3 centimeter?

Step-by-step explanation:

The Volume of a Sphere

The volume of a sphere of radius r is given by:

A. )

If the diameter of the sphere is d, the radius is r=d/2. Substituting:

Operating

Simplifying

B.)

The diameter of the sphere is 2/3 cm, thus the volume is:

Operating:

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

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step-by-step explanation: