Question
A cone is marked with a height of 12 centimeters and a diameter of 11 centimeters, both shown as perpendicular dotted lines. The slant height is 9 centimeters.
What is the height of the right circular cone?
What is the height of the right circular cone?
Answers
Answer
Wrong
Answered by
GPT 3.5
In a right circular cone, the slant height, height, and radius form a right triangle.
We can use the Pythagorean theorem to find the height of the cone.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the height of the cone is one of the legs, the slant height is the hypotenuse, and the radius is the other leg.
Let's call the height of the cone h, the slant height s, and the radius r.
We are given that the slant height is 9 centimeters.
Applying the Pythagorean theorem, we have:
h^2 + r^2 = s^2
Since the diameter is given to be 11 centimeters, the radius is half of that: r = 11/2 = 5.5 centimeters.
Substituting the given values into the equation, we have:
h^2 + (5.5)^2 = 9^2
Simplifying, we have:
h^2 + 30.25 = 81
Subtracting 30.25 from both sides:
h^2 = 50.75
Taking the square root of both sides, we have:
h ≈ 7.11
Therefore, the height of the right circular cone is approximately 7.11 centimeters.
We can use the Pythagorean theorem to find the height of the cone.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the height of the cone is one of the legs, the slant height is the hypotenuse, and the radius is the other leg.
Let's call the height of the cone h, the slant height s, and the radius r.
We are given that the slant height is 9 centimeters.
Applying the Pythagorean theorem, we have:
h^2 + r^2 = s^2
Since the diameter is given to be 11 centimeters, the radius is half of that: r = 11/2 = 5.5 centimeters.
Substituting the given values into the equation, we have:
h^2 + (5.5)^2 = 9^2
Simplifying, we have:
h^2 + 30.25 = 81
Subtracting 30.25 from both sides:
h^2 = 50.75
Taking the square root of both sides, we have:
h ≈ 7.11
Therefore, the height of the right circular cone is approximately 7.11 centimeters.
Answered by
GPT 3.5
Apologies for the incorrect response.
To find the height of the right circular cone, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the height of the cone is the vertical side, the slant height is the hypotenuse, and the radius is the base side.
Given that the slant height is 9 centimeters, and the radius (half of the diameter) is 11/2 = 5.5 centimeters.
Let's call the height of the cone h.
Applying the Pythagorean theorem, we have:
h^2 + 5.5^2 = 9^2
h^2 + 30.25 = 81
Subtracting 30.25 from both sides:
h^2 = 50.75
Taking the square root of both sides, we have:
h ≈ 7.12
Therefore, the height of the right circular cone is approximately 7.12 centimeters.
To find the height of the right circular cone, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the height of the cone is the vertical side, the slant height is the hypotenuse, and the radius is the base side.
Given that the slant height is 9 centimeters, and the radius (half of the diameter) is 11/2 = 5.5 centimeters.
Let's call the height of the cone h.
Applying the Pythagorean theorem, we have:
h^2 + 5.5^2 = 9^2
h^2 + 30.25 = 81
Subtracting 30.25 from both sides:
h^2 = 50.75
Taking the square root of both sides, we have:
h ≈ 7.12
Therefore, the height of the right circular cone is approximately 7.12 centimeters.