If the radius of a right circular cylinder is tripled and its altitude is cut in half, then the ratio of the volume of the original cylinder to the volume of the altered cylinder is?
original radius and height : r and h
volume = π r^2 h
new radius = 3r
new height = h/2
new volume = π (3r)^2 (h/2)
= (9/2) π r^2 h
ratio of old volume to new volume
= πr^2 h : (9/2) π r^2 h
= 1 : 9/2
= 2 : 9
dsaf
Well, if the radius of the original cylinder is tripled, it means it got three times bigger. But if the altitude is cut in half, it means it got two times smaller. So, let's call the original volume "V" and the altered volume "A".
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the altitude.
Now, if the radius is tripled, it becomes 3r, and if the altitude is halved, it becomes 0.5h. So, we have the altered volume, A = π(3r)^2(0.5h).
Simplifying that gives us A = π(9r^2)(0.5h), which can be further simplified as A = 4.5πr^2h.
Now, we can compare the original volume, V, and the altered volume, A, to find the ratio. It is V/A = V/(4.5πr^2h).
So, the ratio of the volume of the original cylinder to the volume of the altered cylinder is 1/(4.5π).
Hope that calculation didn't make your head spin like a cylinder!
To find the ratio of the volume of the original cylinder to the altered cylinder, we need to compare their volumes.
Let's denote the radius of the original cylinder as "r" and the altitude as "h".
Thus, the volume of the original cylinder is V₁ = πr²h.
According to the given information, the radius is tripled, so the new radius is 3r.
The altitude is cut in half, so the new altitude is h/2.
The volume of the altered cylinder is V₂ = π(3r)²(h/2).
Simplifying, we have:
V₂ = π(9r²)(h/2)
= 4.5πr²h
To find the ratio of V₁ to V₂, we divide V₁ by V₂:
V₁/V₂ = (πr²h) / (4.5πr²h)
= 1 / 4.5
= 1/9
Therefore, the ratio of the volume of the original cylinder to the volume of the altered cylinder is 1/9.
To find the ratio of the volume of the original cylinder to the volume of the altered cylinder, we need to calculate the individual volumes of both cylinders and then divide them to get the ratio.
Let's assume the original cylinder has radius "r" and altitude "h". Therefore, its volume can be calculated using the formula:
Volume of original cylinder = π * r^2 * h
Now, according to the given information, the radius is tripled, which means the new radius (r') is three times the original radius (r). So, r' = 3r.
Additionally, the altitude is cut in half, which means the new altitude (h') is half of the original altitude (h). So, h' = h/2.
Now, let's calculate the volume of the altered cylinder using the new measurements:
Volume of altered cylinder = π * (r')^2 * h'
= π * (3r)^2 * (h/2)
= π * 9r^2 * (h/2)
= π * 9/2 * r^2 * h
To find the ratio, we can divide the volume of the original cylinder by the volume of the altered cylinder:
Ratio = (Volume of original cylinder) / (Volume of altered cylinder)
= (π * r^2 * h) / (π * 9/2 * r^2 * h)
= (1 * r^2 * h) / (9/2 * r^2 * h)
= 2/9
Therefore, the ratio of the volume of the original cylinder to the volume of the altered cylinder is 2/9.