Question
1. Find the length of the height of the cone
d = 10 cm wide
13 cm high
d = 10 cm wide
13 cm high
Answers
GPT 3.5
To find the length of the height of the cone, we can use the Pythagorean theorem.
First, let's label the dimensions of the cone:
- Diameter (d) = 10 cm
- Height (h) = 13 cm
The radius of the cone (r) can be found by dividing the diameter by 2:
r = d/2 = 10 cm / 2 = 5 cm
Now, we can use the Pythagorean theorem to find the length of the height (h) of the cone.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite to the right angle) is equal to the sum of the squares of the other two sides.
In the case of the cone, the radius (r) is one of the sides of the right-angled triangle, and the height (h) is the hypotenuse.
Using the Pythagorean theorem:
h^2 = r^2 + d^2
Substituting the values:
h^2 = 5 cm^2 + 13 cm^2
h^2 = 25 cm^2 + 169 cm^2
h^2 = 194 cm^2
To find h, we need to take the square root of both sides:
h = √194 cm
Therefore, the length of the height of the cone is approximately 13.93 cm.
First, let's label the dimensions of the cone:
- Diameter (d) = 10 cm
- Height (h) = 13 cm
The radius of the cone (r) can be found by dividing the diameter by 2:
r = d/2 = 10 cm / 2 = 5 cm
Now, we can use the Pythagorean theorem to find the length of the height (h) of the cone.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite to the right angle) is equal to the sum of the squares of the other two sides.
In the case of the cone, the radius (r) is one of the sides of the right-angled triangle, and the height (h) is the hypotenuse.
Using the Pythagorean theorem:
h^2 = r^2 + d^2
Substituting the values:
h^2 = 5 cm^2 + 13 cm^2
h^2 = 25 cm^2 + 169 cm^2
h^2 = 194 cm^2
To find h, we need to take the square root of both sides:
h = √194 cm
Therefore, the length of the height of the cone is approximately 13.93 cm.