a cone full of water has been poured intoa cylinder. what is the depth of thewater in the cylinder?
the cone has a height of 15m and a diameter of 20m.
the cylinder also has a diameter of 20m and the amount of water in the cylinder is d meters high.
volume of a cone is 1/3 base * height
volume of a cylinder = base * height
so, a cylinder has 3 times the volume of a cylinder of the same base area.
so, the water height in the cylinder is 1/3 the height of the cone is d = 5m.
d= 15 m
To determine the depth of the water in the cylinder, we can use the concept of similar triangles.
In the given scenario, we have a cone and a cylinder with the same diameter. The height of the cone is 15m, and the diameter is 20m. The cylinder's diameter is also 20m, and the height of the water in the cylinder is d meters.
Let's start by finding the relationship between the heights of the cone and the cylinder. Since the diameters are the same, the radius of both the cone and the cylinder is half of the diameter, which is 10m.
Now, let's consider the height of the water in the cylinder, which is d meters. To find the equivalent height in the cone, we need to determine the ratio between the height of the water in the cone and the height of the cone itself.
The ratio of the heights will be the same as the ratio of the radii. Let's denote the height of the water in the cone as h and set up the equation:
h / 15 = (d /10)
To find the depth of the water in the cylinder (d), we can rearrange the equation:
d = (h / 15) * 10
Since the cone is full of water, the height of the water in the cone (h) will be the same as the height of the cone itself, which is 15m. Therefore, substituting the value of h, we get:
d = (15 / 15) * 10
d = 1 * 10
d = 10
So, the depth of the water in the cylinder is 10 meters.