If a cylinder’s radius and height are each shrunk down to a third of the original size, what would be the formula to find the modified surface area?

Question

anonymous · Answer

A.$$\frac{ 1 }{ 9 } \pi r^2 + \frac{ 2 }{ 3 } \pi r h$$
B.$$\frac{ 2 }{ 3 } \pi r^2 + \frac{ 2 }{ 3 } \pi r h$$
C.$$\frac{ 2 }{ 3 } \pi r^2 + \frac{ 1 }{ 3 } \pi r h$$
D.$$\frac{ 2 }{ 9 } \pi r^2 + \frac{ 2 }{ 9 } \pi r h$$

mathstudent55 · Answer

What is the formula for the surface area of a cylinder?

anonymous · Answer

$$2 \pi r h + 2 \pi r^2$$

mathstudent55 · Answer

|dw:1427461899709:dw|

mathstudent55 · Answer

Correct.
Now use the formula you have and replace r with r/3, and replace h with h/3.
Then simplify.

anonymous · Answer

so itd be B?

mathstudent55 · Answer

I don't know until I try.
Let's see.

mathstudent55 · Answer

Original formula:

$SA = 2 \pi r h + 2 \pi r^2$

No let r = r/3, and h = h/3:

$SA = 2 \pi \dfrac{r}{3} h + 2 \pi \left(\dfrac{r}{3} \right) ^2$

$SA = \dfrac{2}{3} \pi r h + \dfrac{2}{9} \pi r^2$

mathstudent55 · Answer

Did you copy all your choices correctly?

anonymous · Answer

yes

mathstudent55 · Answer

none of the choices are correct.

anonymous · Answer

it was d

mathstudent55 · Answer

Then you copied d incorrectly above.
Only one fraction has a denominator of 9, not both.
Since the radius is squared in the formula of the area of a circle, the part of the surface area that comes from the bases has a denominator of 9 since (r/3)^2 = r^2/9.
The lateral area uses the circumference of the base. When the radius becomes 1/3 of the radius, you just use r/3 in the circumference formula. There is no squaring of the radius in the circumference formula, so the denominator remains 3, not 9.