anon1 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.
This is a "what is the value of..." DS question. In this type of question, a statement will be sufficient only if it leads to a single value of the variable (or expression) you're asked about.
Remember, surface area of a cylinder = 2 π r² + 2 π r h where r is the radius of the cylinder, h is its height and π is a constant. The ratio between the surface areas of the two cylinders can be determined either by calculating the two surface areas or by identifying relationships between r and h of the two.
Stat. (1) + (2) Combined, you get the relationship between the radii as well as heights of the two cylinders. Let 2r be the radius of cylinder A and r be the radius of cylinder B as per Stat. (1), and let h be the height of both cylinders as the height of cylinder A is equal to that of cylinder B. By plugging in these in the formula of the surface area of a cylinder, you find that the surface area of cylinder A = 8 π r² + 4 π r h and that of cylinder B = 2 π r² + 2π r h. It is not possible to determine the ratio between the surface areas of cylinder A and B without knowing the specific values of r and h.
Stat.(1) + (2)->IS->E.
So I understand the math and was able to get to the point of cylinder A = 8 π r² + 4 π r h and that of cylinder B = 2 π r² + 2π r h.
But the provided solution only says that "It is not possible to determine the ratio between the surface areas of cylinder A and B without knowing the specific values of r and h."
I don't understand why. I chose C because we're given the relationship between the two diameters, in addition to H.
Could someone help me to understand?
\(Surface area of A = 2*pi*2r*(2r+h)\)
\(Surface area of B = 2*pi*r*(r+h)\)
\(\frac{Area_A}{Area_B} = \frac{2*pi*2r*(2r+h)}{2*pi*r*(r+h)}\)
\(= \frac{2*(2r+h)}{(r+h)}\)
So to know the ratio, we need atleast r in terms of h. What makes a hemisphere,cylinder, cone, and cuboid different from a sphere and square is the presence of a "+" in the calculation of the total surface area.
While the given data would have been sufficient had the cylinders been open at the top and bottom, it is not sufficient in the case of normal cylinders.
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