The cones below are similar, although not drawn to scale.
What is the length of the radius of the larger cone?
The height of the smaller cone is 18 and the radius is 6. The height of the larger cone is 27 and the radius is unknown.
A- 4
B- 6
C- 9
D- 12
Please help!
9
6*3/2 = 9
the heights are in the ratio 27:18 = 3:2
so, the radii are in the same ratio. So, what is x if x:6 = 3:2 ?
To find the length of the radius of the larger cone, we can set up a proportion using the height and radius of both cones.
Let's denote the length of the radius of the larger cone as "r".
Using the given information:
For the smaller cone:
Height = 18
Radius = 6
For the larger cone:
Height = 27
Radius = r
The proportion we can set up is:
(height of smaller cone)/(height of larger cone) = (radius of smaller cone)/(radius of larger cone)
Substituting the given values, we get:
18/27 = 6/r
Now, we can solve for "r" by cross-multiplying and then solving for "r":
18r = 27 * 6
18r = 162
r = 162/18
r = 9
Therefore, the length of the radius of the larger cone is 9.
So, the correct answer is C- 9.
To find the length of the radius of the larger cone, we can use the fact that similar cones have proportional dimensions.
Here's how to solve it step by step:
1. Set up a proportion using the heights (h) and radii (r) of each cone. Since the cones are similar, the ratios of the corresponding dimensions are equal. So, we have:
(height of smaller cone) / (height of larger cone) = (radius of smaller cone) / (radius of larger cone)
substituting the given values, we get:
18 / 27 = 6 / (radius of larger cone)
2. Simplify the equation by dividing both sides by 9:
2 / 3 = 6 / (radius of larger cone)
3. Cross multiply:
2 * (radius of larger cone) = 3 * 6
2 * (radius of larger cone) = 18
4. Solve for the radius of the larger cone by dividing both sides by 2:
(radius of larger cone) = 18 / 2
(radius of larger cone) = 9
Therefore, the length of the radius of the larger cone is 9. So the correct answer is option C- 9.