Thread: SAT problem help

For Pre calc cannot figure this out even though I know it is simple

A standard 8 1/2 X 11 inch sheet of paper is rolled along its short side to for a cylinder that is 8 1/2 inches high

A second sheet of standard 8 1/2 X 11 inch paper is rolled along its long side to form a second cyliner which if 11 inches high

There is no overlap

A. Will the taller cylinder have the same surface area, greater surface rea, or less surface area than the shorter cylinder? Explain
B. Will the taller cylinder have the same volume, greater volume, or less volume than the shorter cylinder? Explain
C. If a shett 11 X 17 inches paper was used to make a cylinder 17 inches tall, how would its volume and surface area compare to the volume and surface area of the 8 1/2 inch tall cylinder? Explain

Originally Posted by mets9131

For Pre calc cannot figure this out even though I know it is simple

A standard 8 1/2 X 11 inch sheet of paper is rolled along its short side to for a cylinder that is 8 1/2 inches high

A second sheet of standard 8 1/2 X 11 inch paper is rolled along its long side to form a second cyliner which if 11 inches high

There is no overlap

A. Will the taller cylinder have the same surface area, greater surface rea, or less surface area than the shorter cylinder? Explain
B. Will the taller cylinder have the same volume, greater volume, or less volume than the shorter cylinder? Explain

I shall answer the first two.

A.) The same since the area of the sheet is the same in both the cylinders the surface area is the same.

B.)The volume of the short cylinder is,
V=(1/3)pi(5.5)^2(8.5)=269.26 cubic inches

The volume of the tall cyclinder is,
V=(1/3)pi(4.25)^2(11)=208.065 cubic inches

Thus the shorter has more volume.

Originally Posted by mets9131

For Pre calc cannot figure this out even though I know it is simple

A standard 8 1/2 X 11 inch sheet of paper is rolled along its short side to for a cylinder that is 8 1/2 inches high

the it is rolled along its long side!

Originally Posted by mets9131

A second sheet of standard 8 1/2 X 11 inch paper is rolled along its long side to form a second cyliner which if 11 inches high

the it is rolled along its short side!

Originally Posted by mets9131

There is no overlap

A. Will the taller cylinder have the same surface area, greater surface rea, or less surface area than the shorter cylinder? Explain
B. Will the taller cylinder have the same volume, greater volume, or less volume than the shorter cylinder? Explain
C. If a shett 11 X 17 inches paper was used to make a cylinder 17 inches tall, how would its volume and surface area compare to the volume and surface area of the 8 1/2 inch tall cylinder? Explain

Hi,

to A) Look at THP's reply.

to B) The taller cylinder has the height 11". You have to calculate the radius of the circle at the ground of the cylinder first:

c = 2*pi*r, thus 8.5" = 2*pi*r. Therefore: r ≈ 1.353"

v = pi*r^2*h, thus: v ≈ pi * (1.353")^2 * 11". Therefore v ≈ 63.244 cubic inches

The smaller cylinder has the height 8.5". You have to calculate the radius of the circle at the ground of the cylinder first:

c = 2*pi*r, thus 11" = 2*pi*r. Therefore: r ≈ 1.751"

v = pi*r^2*h, thus: v ≈ pi * (1.751")^2 * 8.5". Therefore v ≈ 81.845 cubic inches

So the higher cylinder has the smaller volume.

EB

Originally Posted by ThePerfectHacker

...

A.) The same since the area of the sheet is the same in both the cylinders the surface area is the same.

...

Hi,

I need some help here: In my opinion the area of the circles of the bottom and the top of a cylinder belong to the surface too.

For my reply I have taken over your approach, but I'm not certain ... so please enlight me.

EB

Originally Posted by earboth

Hi,

I need some help here: In my opinion the area of the circles of the bottom and the top of a cylinder belong to the surface too.

I did not chose to include that for the two circles are not created from the paper itself.

Originally Posted by ThePerfectHacker

I did not chose to include that for the two circles are not created from the paper itself.

Hi,

thank you for this explanation, but...

According to my dictionary the sheet of paper must be the "curved surface". Therefore I believe that the (complete) surface of a cylinder contains the curved surface and two circles.
But maybe the definition of "surface of a solid" is not rigidly clear.

tschüss

EB