Bunuel wrote:

30% of the surface area of a right circular cylinder is shaded. If the diameter of the base of the cylinder is 10 and the height is 4, what is the surface area of the unshaded region?

A. \(27\pi\)

B. \(40\pi\)

C. \(63\pi\)

D. \(70\pi\)

E. \(90\pi\)

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cylinderSA.jpg [ 24.26 KiB | Viewed 302 times ]
The formula for the surface area of a right circular cylinder* is

\(2πr^2+ 2πrh\)Height = \(4\)

Diameter = \(10\), so radius, \(r=5\)

S.A. = \(2*5^2*π + 2*5*π*4\)

Total S.A. = \((50π+40π)=90π\)70% is unshaded: \(90π*.7=63π\)

Answer C

•Imagine that a label on a can is unwrapped.

The label was wrapped around a circular can: one length of the rectangle is circumference

The other length of the rectangle is the label's height.

Multiply those lengths (essentially, L * W) to get the area of the label: \(2\pi r * h\)

•Then add the area of the two circles (top and bottom of cylinder): \(2*( \pi r^2)\)
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In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"