The cake is shaped as a cylinder of radius 9 inches and height of 4 inches
The rule of the volume of the cylinder is
[tex]V=\pi r^2h[/tex]
r is the radius
h is the height
Since the diameter is 9, then
r = 9/2 = 4.5
Since the height is 4
h = 4
Substitute them in the rule
[tex]\begin{gathered} V=\pi(4.5^2)(4) \\ \\ V=\pi(20.25)(4) \\ \\ V=254.469\text{ in}^3 \end{gathered}[/tex]
The volume of the cake is 254.469 cubic inches
A) The answer is 254.469 in.^3
Since the length of the arc is 3 inches, then the volume of each part is
[tex]\begin{gathered} V=\frac{3}{\pi(9)}\times254.469 \\ \\ V=26.99999 \\ \\ V\approx27\text{ in}^3 \end{gathered}[/tex]
B) The answer is 27 in^3 the 2nd choice
C)
We will divide the volume of one piece by the volume of the cake to find the probability of one piece
[tex]\begin{gathered} P=\frac{27}{254.469}\times100 \\ \\ P=10.6\text{ \%} \end{gathered}[/tex]
The answer is 10.6%
D)
To find the probability of the 3 pieces is
[tex]\begin{gathered} P(3)=3\times10.6103 \\ \\ P(3)=31.8\text{ \%} \end{gathered}[/tex]
The answer is 31.8%, 3rd option
E)
The probability of the fourth piece is
[tex]P(4th)=100\text{ \% - 31.8\% = 68.2\%}[/tex]
Then if the probability of the 4th piece increase, then the probability of the other 3 pieces will decrease
