Answer:
See Below
Step-by-step explanation:
The surface area of cylinder is given by the formula:
[tex]SA=2\pi r^2 + 2\pi r h[/tex]
Where
r is radius ( diameter is 4, so radius is 4/2 = 2)
h is height ( h = 9)
Lets find original surface are:
[tex]SA=2\pi r^2 + 2\pi r h\\SA=2\pi (2)^2 + 2\pi (2) (9)\\SA=8\pi +36\pi\\SA=44\pi[/tex]
Halving diameter:
diameter would be 4/2 = 2, so radius would be 2/2 = 1
So, SA would be:
[tex]SA=2\pi r^2 + 2\pi r h\\SA=2\pi (1)^2 + 2\pi (1) (9)\\SA=2\pi +18\pi\\SA=20\pi[/tex]
Halving height:
Height is 9, halving would make it 9/2 = 4.5
Now, calculating new SA:
[tex]SA=2\pi r^2 + 2\pi r h\\SA=2\pi (2)^2 + 2\pi (2) (4.5)\\SA=8\pi + 18\pi\\SA= 26\pi[/tex]
Original SA is [tex]44\pi[/tex],
Halving diameter makes it [tex]20\pi[/tex]
Halving height makes it [tex]26\pi[/tex]
So, halving diameter does not have same effect as halving height.
