Rectangular label wrapped around cylinder

[expert]

Hi guys. Could you please give me your reasoning of the answer for the following question ?

When a rectangular label, 21.5 centimeters long, is wrapped around the curved surface of a solid circular cylinder with its shorter ends overlapping, it exactly covers the curved surface. What is the volume of the cylinder in cubic centimeters, of the thickness of the label is ignored ?

(1) The label overlap is 0.5 centimeters.
(2) The width of the label if 7.5 centimeters.

Thanks!

[vittalgmat]

IMO C.
Here is how I approached.

The length of the strip is 21.5 cm. Imagine that it is rolled into a cylinder with some part of the strip overlapping. The overlapping part should not be concerned for finding the volume.

We know that volume of cylinder is Pi*r^2 * height.

Stmt 1 tells us to ignore 0.5 cms of the length.
so circumferance of the cylinder = 21cms.
from that we can find r
ie 2*Pi*r = 21.
= 2* 22/7 * r = 21.
So r = (21 *7) /(2 *22) -(1)

So stmt 1 gives us a value of r. ( No need to calculate the value coz this is a DS problem).

But still insufficient coz we dont know the width of the strip , which is the height of the cylinder.

so insufficient.


Stmt 2. this gives us width of the strip , which is height h.

but no r. Hence not sufficient.

Considering them together, we get both r and h. So can find the volume.

So C.


(my perspective: this is a relatively easy problem, in the 400 -500 range.)


Ht Helps
-V

[expert]

Thank you, vittalgmat. Could you please tell me what part of the question stands for "width of the strip == height of cylinder" ? Is it "exactly covers the curved surface" ?

[vittalgmat]

Imagine a rectangular strip 21 cms long . If u roll hte strip along the long side, the longer side form a circle.

From the problem "the shorter ends overlapping" refers to the width.
Also "exactly covers the curved surface" means that width of the strip == height of cylinder.

Ht helps