two cylinders have identical bases with differnt lengths.the length of shorte cylinder is x where as the length of longer cylinder is 2x.which statement is true
1.the shorter cylinder has one half the surface area of the taller cylinder for all values of x.
2.the shorter cylinder has same surface area as the taller cylinder for some values of x.
3.The shorter cylinder has one half the volume of the larger cylinder for all values of x
4.The shorter cylinder has same volume as the larger cylinder for some values of x.
surface area = area of base and top (same for both) + height*2 pi r
so not the same and not twice
volume = area of base * height
ah ha, twice if you double height
which statement is true
I told you.
I dint understood .give me the number of the statement
Thanks a loooooooooooot
To determine which statement is true, we can compare the surface area and volume formulas for cylinders and examine how they change with the given length ratio.
The formula to calculate the surface area of a cylinder is given by A = 2πr(r + h), where r is the radius of the base and h is the height (length) of the cylinder.
The formula to calculate the volume of a cylinder is given by V = πr^2h.
Let's analyze each statement:
1. The shorter cylinder has one-half the surface area of the taller cylinder for all values of x.
To verify this statement, we need to compare the surface areas of the two cylinders. Since the bases are identical, the only difference is in the lengths of the cylinders. Given that the length of the shorter cylinder is x and the length of the longer cylinder is 2x, the ratio of their lengths is 1:2.
Using the formula for the surface area, we can see that the height term increases the surface area linearly, meaning that if the length of the shorter cylinder is halved, its surface area will also be halved. Therefore, statement 1 is true.
2. The shorter cylinder has the same surface area as the taller cylinder for some values of x.
To verify this statement, we need to determine if there are any values of x for which the two cylinders have the same surface area. Since the bases are identical and the only difference is in the lengths, to have the same surface area, the height term must be equal too. However, since the length of the shorter cylinder is halved compared to the longer cylinder, there are no values of x that would make the surface areas identical. Therefore, statement 2 is false.
3. The shorter cylinder has one-half the volume of the larger cylinder for all values of x.
To verify this statement, we need to compare the volumes of the two cylinders. The volume is directly proportional to the height (length) of the cylinder. Since the length of the shorter cylinder is x and the length of the longer cylinder is 2x, their height ratio is again 1:2. Since the volume formula includes height as a linear term, halving the height of the shorter cylinder will result in halving its volume compared to the taller cylinder. Therefore, statement 3 is true.
4. The shorter cylinder has the same volume as the larger cylinder for some values of x.
To verify this statement, we need to determine if there are any values of x that would make the volumes of both cylinders equal. However, since the height of the shorter cylinder is always half of the taller cylinder, there are no values of x that will result in the same volume for both cylinders. Therefore, statement 4 is false.
In conclusion:
- Statement 1 is true.
- Statement 2 is false.
- Statement 3 is true.
- Statement 4 is false.