A mailing tube is 25" long with a diameter of 4". What is the volume of a similar tube that has a diameter 50% larger than the original tube?

So, the new tubes diameter would be 6. So to figure the volume do i take 3.14 *36 or??

Yes, the new tube's base area is 36 pi. The question is, what happens to the length? When they say the tubes are "similar", that should mean that the length also increases 50%, to 37.5 inches. But perhaps they mean for the length to stay the same. The problem should have been more clearly worded.

To find the volume of a cylindrical object, you need to multiply the area of the base by the height. In this case, the base is a circle.

First, let's find the radius of the original tube. The diameter is given as 4", so the radius would be half of that, which is 2".

Now, calculate the volume of the original tube using the formula for the volume of a cylinder: V = π * r^2 * h, where V represents volume, π (pi) is a mathematical constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the tube.

For the original tube:
radius (r) = 2"
height (h) = 25"

V = 3.14159 * (2^2) * 25

V = 3.14159 * 4 * 25

V ≈ 314.159 cubic inches

Now, let's find the volume of the new tube, which has a diameter 50% larger than the original tube. If the original diameter is 4", a 50% increase would be an additional 2" (50% of 4").

Thus, the new diameter would be 4" + 2" = 6", which means the radius would be 3" (half of 6").

Using the same volume formula:

For the new tube:
radius (r) = 3"
height (h) = 25"

V = 3.14159 * (3^2) * 25

V = 3.14159 * 9 * 25

V ≈ 706.8585 cubic inches

Therefore, the volume of the new tube, with a diameter 50% larger than the original, is approximately 706.8585 cubic inches.