ratio of total surface area to the curved surface area of a right circular cylinder 3:2 find the volume if its total surface area is 14784 cm2.

Question

ratio of total surface area to the curved surface area of a right circular cylinder 3:2 find the volume if its total surface area is 14784 cm².

Answer 1

A right circular cylinder is just a can. Don't ever get stuck on the terminology. That'll make you tear your hair out. LOL

 

The surface area for that? Either end is a circle, π r^2.

The "curved surface" is the circumference of the circle times height,

2 π r h.

 

Ratio of total to curved:

 

2 π r (r + h) / 2 π r ^2 == (r + h) / r

 

And if this is 3:2, you'll find that h = r/2. Check my math on that if you don't believe me.

 

That makes the total surface area 3 π r^2. If that is 14784 cm^2 then r = about 39.6 cm.

 

Now, as for the volume. That's the circle area times height:

 

V = π r^2 h = π r^3 / 2 = about 97589 cm^3. Little rounding error there, though I carried π out to eight decimal places. Solve the problem symbolically first and π drops out, giving you more of an exact answer.