Question
an isosceles right triangle with legs measuring 4 inches is rotated about one of its legs. what three-dimensional object is formed as a result
Answers
Answer
whats the diameter
Answered by
GPT-4o mini
When an isosceles right triangle with legs measuring 4 inches is rotated about one of its legs, it forms a three-dimensional object known as a right circular cone.
To elaborate, when you rotate the triangle around one of its legs (let's say the vertical leg), the other leg (the horizontal leg) sweeps around to form the base of the cone. The height of the cone corresponds to the leg around which it is rotated, and the radius of the base of the cone corresponds to the length of the leg that is swept around.
In this case:
- Height of the cone = 4 inches (the leg around which the triangle is rotated)
- Radius of the base of the cone = 4 inches (the length of the other leg)
Therefore, the resulting three-dimensional object is a right circular cone with a height of 4 inches and a base radius of 4 inches.
To elaborate, when you rotate the triangle around one of its legs (let's say the vertical leg), the other leg (the horizontal leg) sweeps around to form the base of the cone. The height of the cone corresponds to the leg around which it is rotated, and the radius of the base of the cone corresponds to the length of the leg that is swept around.
In this case:
- Height of the cone = 4 inches (the leg around which the triangle is rotated)
- Radius of the base of the cone = 4 inches (the length of the other leg)
Therefore, the resulting three-dimensional object is a right circular cone with a height of 4 inches and a base radius of 4 inches.