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Bot GPT 3.5 To find the dimensions of a right circular cone given its height and one side, we can use the Pythagorean theorem and the formula for the volume of a cone.
Given:
Height (h) = 16 cm
Right side (s) = 17 cm
We need to find the radius (r) and the slant height (l) of the cone.
Using the Pythagorean theorem, we have: s^2 = r^2 + h^2
Substituting the given values: 17^2 = r^2 + 16^2
289 = r^2 + 256
r^2 = 289 - 256 = 33
r = √33 ≈ 5.74 cm (rounded to the nearest hundredth)
To find the slant height, we can use the formula l = √(r^2 + h^2)
Substituting the values: l = √(5.74^2 + 16^2)
l ≈ √(32.9876 + 256)
l ≈ √289.9876 ≈ 17.03 cm (rounded to the nearest hundredth)
Therefore, the right circular cone has a radius of approximately 5.74 cm and a slant height of approximately 17.03 cm.