Question
9 cm 12 cm What is the height of the right cone ?
Answers
GPT 3.5
To find the height of a cone, you need to use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the height of the right cone is one of the legs of a right triangle. Let's use the formula:
a² + b² = c²
where a = height, b = radius (half of the diameter), and c = slant height.
We know that the radius is half of the diameter, so the radius of the cone is 12/2 = 6 cm.
Now, we can apply the formula:
a² + 6² = 9²
a² + 36 = 81
a² = 81 - 36
a² = 45
Taking the square root of both sides, we find:
a ≈ √45 ≈ 6.71 cm
So, the height of the right cone is approximately 6.71 cm.
In this case, the height of the right cone is one of the legs of a right triangle. Let's use the formula:
a² + b² = c²
where a = height, b = radius (half of the diameter), and c = slant height.
We know that the radius is half of the diameter, so the radius of the cone is 12/2 = 6 cm.
Now, we can apply the formula:
a² + 6² = 9²
a² + 36 = 81
a² = 81 - 36
a² = 45
Taking the square root of both sides, we find:
a ≈ √45 ≈ 6.71 cm
So, the height of the right cone is approximately 6.71 cm.