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valina [46]
3 years ago
7

A cylinder has diameter of 4ft and a height of 9ft. Explain whether halving the diameter has the same effect on the surface area

as halving the height.
Mathematics
1 answer:
elena55 [62]3 years ago
5 0

Answer:

See Below

Step-by-step explanation:

The surface area of cylinder is given by the formula:

SA=2\pi r^2 + 2\pi r h

Where

r is radius ( diameter is 4, so radius is 4/2 = 2)

h is height ( h = 9)

Lets find original surface are:

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

<u>Halving diameter:</u>

diameter would be 4/2 = 2, so radius would be 2/2 = 1

So, SA would be:

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

<u>Halving height:</u>

Height is 9, halving would make it 9/2 = 4.5

Now, calculating new SA:

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

Original SA is 44\pi,

Halving diameter makes it 20\pi

Halving height makes it 26\pi

So, halving diameter does not have same effect as halving height.

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