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The surface area of cylinder A is how many times the surface area of

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Bunuel
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The surface area of cylinder A is how many times the surface area of [#permalink] New post   26 Jan 2023, 02:30
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E

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85% (hard)

Question Stats:

16% (01:16) correct 84% (01:04) wrong based on 43 sessions
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The surface area of cylinder A is how many times the surface area of cylinder B?

(1) The diameter of A is twice the diameter of B.
(2) The height of A is equal to the height of B.


Another challenging geometry question.

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E
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divyadna
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Re: The surface area of cylinder A is how many times the surface area of [#permalink] New post   26 Jan 2023, 03:17
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The surface area of cylinder A is how many times the surface area of cylinder B?

(1) The diameter of A is twice the diameter of B.

SA of cylinder= 2πrh+2πr^2= 2πr(h+r)
SA of A:SA of B= 2π.2r (h+2r)/2πr(h+r)

Statement I is clearly insufficient.
Reject A and D.

(2) The height of A is equal to the height of B.
SA of cylinder= 2πrh+2πr^2= 2πr(h+r)
SA of A:SA of B= 2πR(h+R)/2πr(h+r)

Again, statement II is insufficient.

Combining the two statements
SA of cylinder= 2πrh+2πr^2= 2πr(h+r)
SA of A:SA of B= 2π*2r(h+2r)/2πr(h+r)= 2(h+2r)/(h+r)

Statement I and Statement II together are insufficient.

Ans is option E

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Re: The surface area of cylinder A is how many times the surface area of [#permalink] New post   26 Jan 2023, 07:11
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Area of a cylinder is the sum of the areas of all its surfaces 2 times area of the base+area of rectangle= 2*(2πr) + 2πr*h

(I) we do not know the height of neither cylinder. INSUFFICINET
(II)we know the height but not the diameter of both cylinder. INSUFFICENT

(I)y(II) since they are asking how many times is A from B we can assign a value for B radius, let's say is 2, and we know by (I) that diameter of A is twice the diameter of B so should be 4. Based on 2 we know they have the same height so lets call it 10.

so area of A = 2(2π4)+2π4*10= 16π+80π=96π
area of B =2(2π2)+2π2*10=8π+40π=48π

now a/b=96π/48π= 2

so area of A is twice the area of B

IMO C
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Re: The surface area of cylinder A is how many times the surface area of [#permalink] New post   26 Jan 2023, 13:31
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Bunuel wrote:
The surface area of cylinder A is how many times the surface area of cylinder B?

(1) The diameter of A is twice the diameter of B.
(2) The height of A is equal to the height of B.


Total Surface Area of a Cylinder = \(2 * \pi * r^2 + 2 * \pi * r * h\)
= \(2 \pi r (r + h)\)

Statement 1 and Statement 2 are individually not sufficient as only one aspect of the dimension is provided.

Combined

Cylinder A :
  • Radius = 2r
  • Height = h

Cylinder B:
  • Radius = r
  • Height = h

\(\frac{TSA_A }{ TSA_B} = \frac{2 \pi *2r (2r + h) }{ 2 \pi r (r + h)}\)

\(\frac{TSA_A }{ TSA_B} = \frac{2(2r + h) }{ (r + h)}\)

As we cannot solve this further. The statements combined are not sufficient.

Option E
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Re: The surface area of cylinder A is how many times the surface area of [#permalink]
26 Jan 2023, 13:31
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Bunuel
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