radius is 4.5 cm and height 21 cm is cut into a cone of height 14 cm . find the radius of the smaller cone
I fail to see how a cone of height 21 can be cut into a cone of height 14.
Better explain things a bit more.
Well, this sounds like a case of "cone-undrum"! Let's solve it step by step.
We have a larger cone with a radius of 4.5 cm and a height of 21 cm. Now, if we cut this cone down to a height of 14 cm, we're essentially creating a smaller cone.
To find the radius of the smaller cone, we can use the concept of similar triangles. Since the ratio of the heights of the two cones is the same as the ratio of their radii, we can set up the following equation:
(21 cm) / (4.5 cm) = (14 cm) / (smaller cone's radius)
Now, let's do some math to find the radius of the smaller cone:
(21 cm) / (4.5 cm) = (14 cm) / (smaller cone's radius)
Cross-multiplying gives us:
(21 cm) * (smaller cone's radius) = (4.5 cm) * (14 cm)
Now, let's divide both sides by 21 cm and simplify:
(smaller cone's radius) = (4.5 cm) * (14 cm) / (21 cm)
Calculating this gives us:
(smaller cone's radius) = 3 cm
Ta-da! The radius of the smaller cone is 3 cm. Keep in mind though, my calculations could be a bit "circusy," so it's always a good idea to double-check!
To find the radius of the smaller cone, we can use the concept of similar triangles and ratios.
Let's denote the radius of the smaller cone as 'r'.
We have the following given measurements:
Radius of the larger cone, R = 4.5 cm
Height of the larger cone, H = 21 cm
Height of the smaller cone, h = 14 cm
Using the concept of similar triangles, we can set up the ratio between the radius of the larger cone and the radius of the smaller cone to be equal to the ratio between the heights:
R / r = H / h
Substituting the values we have:
4.5 / r = 21 / 14
Simplifying the ratio:
4.5 * 14 = 21 * r
63 = 21r
Dividing both sides of the equation by 21:
r = 63 / 21
r = 3
Therefore, the radius of the smaller cone is 3 cm.
To find the radius of the smaller cone, we need to use similar triangles.
First, let's draw a diagram to visualize the situation. We have a larger cone with a radius of 4.5 cm and a height of 21 cm. It is then cut to form a smaller cone with a height of 14 cm.
Now, let's consider the ratio of the heights of the two cones. We have:
Ratio of heights = Height of the smaller cone / Height of the larger cone
Let's plug in the values we have:
Ratio of heights = 14 cm / 21 cm
Simplifying this ratio, we get:
Ratio of heights = 2/3
Now, let's use the ratio of heights to find the ratio of radii. Since the two cones are similar, the ratio of their radii should be the same as the ratio of their heights.
So we have:
Ratio of radii = Ratio of heights = 2/3
Now, let's find the radius of the smaller cone using this ratio.
Radius of the smaller cone = Ratio of radii * Radius of the larger cone
Substituting the given values:
Radius of the smaller cone = (2/3) * 4.5 cm
Simplifying this expression, we get:
Radius of the smaller cone = 3 cm
Therefore, the radius of the smaller cone is 3 cm.