Question

Can you solve please this it one question with multiple parts

Answer 1

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

`V=\pi r^2h`

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

`\begin{gathered} V=\pi(4.5^2)(4) \\ \\ V=\pi(20.25)(4) \\ \\ V=254.469\text{ in}^3 \end{gathered}`

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

`\begin{gathered} V=(3)/(\pi(9))*254.469 \\ \\ V=26.99999 \\ \\ V\approx27\text{ in}^3 \end{gathered}`

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

`\begin{gathered} P=(27)/(254.469)*100 \\ \\ P=10.6\text{ \%} \end{gathered}`

The answer is 10.6%

D)

To find the probability of the 3 pieces is

`\begin{gathered} P(3)=3*10.6103 \\ \\ P(3)=31.8\text{ \%} \end{gathered}`

The answer is 31.8%, 3rd option

E)

The probability of the fourth piece is

`P(4th)=100\text{ \% - 31.8\% = 68.2\%}`

Then if the probability of the 4th piece increase, then the probability of the other 3 pieces will decrease