If a big cylinder has the radius of 24cm and a height of 18cm, what would the height be for the smaller cylinder with 4cm as the radius?
Thank you so much.
Is the volume of the small cylinder the same as the volume of the large cylinder. I think it must be; otherwise, I don't believe you can solve the problem.
Yes.
I've been at this since 3:00 and I'm getting nervous. I really need help.
volume of large cylinder = pi*r^2*h = 3.14(24)^2(18) = ? cc.
For the small cylinder
V = pi*r^2*h
?cc from above = 3.14(4)^2*h
Solve for volume of large cylinder, substitute that for volume of small cylinder and solve for h of small cylinder.
the answers are
A. 3cm
B. 6 cm
C. 9 cm
D. 18 cm
with a radius of 4 cm.
None of those numbers fit. Do you have a picture of the cylinder? Is it a regular (right) cylinder or an ellipsoid cylinder. It must not be a right cylinder. Here is a picture of a right cylinder. You can google image cylinder and see what the ellipsoid one looks like.
To solve this problem, we can use the concept of similar figures. Two figures are similar if they have the same shape but different sizes. Since both cylinders have the same shape (circular base and constant width), we can say that they are similar.
The ratio of the radii of the two cylinders is 24 cm (big cylinder) to 4 cm (small cylinder), which simplifies to 6:1. This means that the height of the small cylinder will also be in a ratio of 6:1 to the height of the big cylinder.
To find the height of the smaller cylinder, we can set up a proportion:
height of big cylinder / height of small cylinder = 6 / 1
18 cm / height of small cylinder = 6 / 1
Cross-multiplying, we get:
18 cm * 1 = 6 * height of small cylinder
Rearranging the equation, we have:
height of small cylinder = (18 cm * 1) / 6
height of small cylinder = 3 cm
Therefore, the height of the smaller cylinder with a radius of 4 cm would be 3 cm.
Remember, we used the concept of similarity and the ratio between the radii of the cylinders to set up and solve the proportion to find the height of the smaller cylinder.