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# 30% of the surface area of a right circular cylinder is shaded. If the

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Math Expert
Joined: 02 Sep 2009
Posts: 51215
30% of the surface area of a right circular cylinder is shaded. If the  [#permalink]

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03 Jul 2018, 08:32
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Difficulty:

55% (hard)

Question Stats:

64% (01:49) correct 36% (01:21) wrong based on 45 sessions

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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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Re: 30% of the surface area of a right circular cylinder is shaded. If the  [#permalink]

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03 Jul 2018, 10:22
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. $$90\pi$$

surface area of the unshaded region=Total surface area of the cylinder-Shaded area(=30% of the total surface area of cylinder)
=S-0.3*S=0.7S=0.7*2*$$\pi$$r(r+h) =1.4*$$\pi$$*5(5+4)=1.4*45*$$\pi$$=63$$\pi$$

Ans.(C)
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30% of the surface area of a right circular cylinder is shaded. If the  [#permalink]

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05 Jul 2018, 22:06
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. $$90\pi$$

Attachment:

cylinderSA.jpg [ 24.26 KiB | Viewed 371 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: $$90π*.7=63π$$

•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): $$2*( \pi r^2)$$
30% of the surface area of a right circular cylinder is shaded. If the &nbs [#permalink] 05 Jul 2018, 22:06
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