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Prompt analysis
Surface area = 2*pi*r(r+h)

Superset
The value will be a positive real number

Translation
In order to find the answer, we need:
1# exact value of r and h.
2# Value of r^2 and rh
3# two equation 2 variables(r and h) to calculate r and h


Statement analysis
St 1: replace r or h with the term in h or r respectively and you will still be left with an expression in one variable
St 2: If you replace h with given expression, after solving, you will be left with 30pi, which is constant. ANSWER

Option B
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What does right circular cylinder mean ? I know how to solve the question but i have heard this term for the first time

Please explain

Thanks

Sent from my SM-N910C using GMAT Club Forum mobile app
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ra5867
What does right circular cylinder mean ? I know how to solve the question but i have heard this term for the first time

Please explain

Thanks

Sent from my SM-N910C using GMAT Club Forum mobile app

A right circular cylinder is a cylinder with the circular bases and with the axis joining the two centers of the bases perpendicular to the planes of the two bases.



Attachment:
right-cylinder.png
right-cylinder.png [ 10.3 KiB | Viewed 30538 times ]
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enigma123
A right circular cylinder has a radius r and a height h. What is the surface area of the cylinder?

(1) r = 2h – 2/h
(2) h = 15/r – r

(1) r = 2h – 2/h
—> 2h + r = 2h^2

Insufficient

(2) h = 15/r – r
—> h + r = 15/r
—> r(h + r) = 15

Surface area = 2*pi*r(r + h) = 2*pi*15 = 30*pi

Sufficient

IMO Option B

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Surface Area of a Cylinder is given by:

TWO of the Circular Base Areas + Area of Rectangle that wraps around the Cylinder =

2 * (pi * (r)^2) + (2pi * r)(h) =

2pi * [ (r)^2 + rh ] = ?

or

2pi*r * (r + h) = ?

if we can find either:

(r)^2 + rh

OR

r * (r + h)

the Statement will be Sufficient


S1: r = 2h - (2/h)

r = (2(h)^2 - 2) / (h)

rh = 2(h)^2 - 2

From this point we could try re-arranging and isolating 1 Variable and Substituting, but we will never be able to get the Variables to cancel out such that we will get a Unique Value for the Surface Area

S1 NOT Sufficient


S2: h = (15/r) - r

h + r = 15/r


Plug this equation above into the Surface Area Equation of:

2pi* r * (r + h) = ?

2pi * r * (15/r) = ?

----the Variable of r Cancels Out ----

2pi * 15 = 30pi = Surface Area of Cylinder

S2 is Sufficient Alone

B
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Bunuel
ra5867
What does right circular cylinder mean ? I know how to solve the question but i have heard this term for the first time

Please explain

Thanks

Sent from my SM-N910C using GMAT Club Forum mobile app

A right circular cylinder is a cylinder with the circular bases and with the axis joining the two centers of the bases perpendicular to the planes of the two bases.



Attachment:
right-cylinder.png

One thing I am wondering is whether there are any "signs" that we can use which tells us whether we should substitute and try to simplify or simply deem a statement insufficient if there are multiple (unknown) variables. The trap in this question is clearly thinking that there are too many unknowns. Should the rule of thumb simply be to always follow through with simplifying?
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when it specifically asked surface area ,then why did we use total surface area ?
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I got the answer right, but it took me ~5 minutes to try to simplify both of the expressions to see whether any of them is sufficient or not. I am curious whether there is a faster way of solving this problem than inserting the information into the area formula and simplifying? If no, how likely is it to see such kind of question in actual exam?
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