A piece of paper has a length of 9 inches and width of 4 inches. The paper is rolled to form the shape of a cylinder. What is the largest possible volume of the cylinder?
there are only two choices
π*2^2*9 = 36π
π(9/2)^2*2 = 81/2 π
The radius will be half the rolled dimension.
To find the largest possible volume of the cylinder that can be formed from the given piece of paper, we need to consider how the paper is rolled.
When a rectangular piece of paper is rolled, the length of the paper becomes the circumference of the base of the cylinder, and the width becomes the height of the cylinder.
In this case, the length of the paper is 9 inches, and the width is 4 inches.
To find the circumference of the base of the cylinder, we use the formula:
Circumference = 2πr,
where r is the radius of the base.
Since the length of the paper becomes the circumference, we can equate these two values:
9 inches = 2πr.
Simplifying this equation, we find:
r = 9 / (2π).
To find the largest possible volume of the cylinder, we use the formula for the volume of a cylinder:
Volume = πr^2h,
where h is the height of the cylinder.
In this case, the width of the paper becomes the height of the cylinder, so we have:
h = 4 inches.
Substituting the values of r and h into the volume formula, we get:
Volume = π(9 / (2π))^2 * 4
Simplifying further, we find:
Volume = 81 / 4 * 4
Volume = 81 cubic inches.
Therefore, the largest possible volume of the cylinder formed from the given piece of paper is 81 cubic inches.