Question

I just can’t understand the question.

Answer 1

Hi,

It is very easy question. (but difficult to explain in a foreign language).

First of all you are suppose to find out the area of a circle, which is a base of a cylinder.

You have at your disposal a sheet of paper 4 x 6 cm.

So there are two possibilities of rolling up this piece of paper: you can roll it along the longest edge, or along the shortest one.

But in the task you are told to roll it along the shortest edge.

Hence you know that the circumference of a circle is 4 cm.

now you have to find the ray of the circle.

it is easy if you know the circumference.

circumference = 2 π * r

r = circumference / 2 π

r = 4 / 2 (3,1415)

r = 4 / 6,283

r = 0,6366

Now, if you know the ray of the circle, you can find the area.

Area = π*r^2

A = 3,1415 * (0,6366)^2

A = 3,1415 * 0,4053

A = 1.2732

i.e. the first option in your task.

Answer 2

With this question you can imagine that you have a 6 cm tall cylindrical container and you take a piece of paper that is 4 cm by 6 cm and wrap it around the cylinder, then take the sheet of paper off whilst maintaining its shape - the paper will form the shape of a cylinder (without a top and bottom) but the two dimensional shape enclosed would be a circle and the area of this circle is what the question is asking.

Now given that the cylinder is 6 cm tall you can assume that the width of the sheet of paper that you would be wrapping around it would also be 6 cm tall and thus the length of that paper would be 4 cm (we are given the dimensions of the sheet as 4 cm x 6 cm) - this length is equal to the circumference of the circle that forms the base of the cylinder:

C = 2πr
4 = 2πr
r = 2/π

Now that we know the radius of the circle we can find its area:

A = πr^2
A = π*(2/π)^2
= 4/π
= 1.27 cm^2 (to two decimal places)

Basically with these questions you should always try to imagine them in a practical situation, it makes it a lot easier in the long run.