Answer:(10/7) times the height of the smaller cone.
Explanation:
AI-generated answer
The candlestick is in the shape of two cones joined at the vertices. The smaller cone has a diameter and sloping side of 7 cm, while the larger cone has a diameter and sloping side of 10 cm. We need to find the height of the candlestick.
To find the height, we can use the concept of similar triangles. Since the two cones are joined at the vertices, the vertical height of the larger cone will be the sum of the heights of the smaller cone and the missing portion of the larger cone.
Let's denote the height of the smaller cone as h1 and the height of the missing portion of the larger cone as h2.
Using the formula for the slope of a cone, we can write:
h1 / 7 = (h1 + h2) / 10
To solve for h2, we can cross-multiply and simplify:
10h1 = 7(h1 + h2)
10h1 = 7h1 + 7h2
3h1 = 7h2
h2 = (3/7)h1
Now, we can find the total height of the candlestick by adding h1 and h2:
Total height = h1 + h2
Total height = h1 + (3/7)h1
Total height = (10/7)h1
Therefore, the total height of the candlestick is (10/7) times the height of the smaller cone.