A cylinder has a surface area of 6pi square feet. a second similar cylinder has a surface area of 150 pi square feet. What is the ratio of the circumferences of the bases of the two cylinders?

Question

A cylinder has a surface area of 6pi square feet. a second similar cylinder has a surface area of 150pi square feet. What is the ratio of the circumferences of the bases of the two cylinders?

Answer 1

ratio of area = (ratio of circumference)²

Ratio of areas = 150π / 6π = 25 / 1

to find the ratio of the circumference take the square root = 5/1 or 1/5 depending on which cylinder is first.

Answer 2

Hi Saja K.

Think for a moment about the dimensional properties of objects. They have linear measurements, area measurements, and volume measurements. Let's call the (linear) scaling factor T: then anything area scales as T^2, and anything volume as T^3.

You were given surface areas; that's an area-type measurement, isn't it. So the ratio 150:6 = 25 represents T^2, and T = 5.

So anything linear (which doesn't mean a straight line necessarily, but anything which has units of length) scales as T, and the ratio respectively here is 1:5 .

Saja, for the future, when you get a problem that doesn't immediately start solving itself in your head (and very few problems will!), analyse: what data am I given; what do I know about such kinds of data (not the numbers themselves, but what they represent, here, areas); what relationships do I know between these types of data and what I need to eventually get as an answer. Frequently, the calculations required will only be unit conversions (mi/hr -> m/s , and so on, which is rather confusingly called "dimensional analysis"), but non infrequently you'll get a slightly higher-level skill called for, such as scaling, special triangle relations, and so on.

-- Cheers, --Mr. d.