Approximate the change in the volume of a right circular cylinder of fixed
radius r equals = 22 22 cm
when its height decreases from
h equals = 10 10 cm to h equals = 9.9 9.9 cm
( upper v (h )equals pi r squared h v(h)=πr2h).

152.1 cm³

Step-by-step explanation:

Change in Volume =  πr²(h₁-h₂)

 Where r = 22 cm

              h₁ = 10 cm    

              h₂ = 9.9 cm  

ΔV =      π x (22)²x (10-9.9)

     =       π  x  484‬ x 0.1

     =    152.11

     ≈  152.1 cm³

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt