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? (1 point)
• cone with a diameter of 8 inches
• cone with a diameter of 4 inches
cylinder with a diameter of 4 inches
• cylinder with a diameter of 8
inches
• cone with a diameter of 8 inches
• cone with a diameter of 4 inches
cylinder with a diameter of 4 inches
• cylinder with a diameter of 8
inches
Answers
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 cone. The height of the cone corresponds to the leg around which it is rotated, which is 4 inches, and the length of the other leg becomes the radius of the base of the cone.
Since the base of the triangle has a length of 4 inches, when rotated, this leg serves as the radius of the base of the cone, which results in a diameter of:
\[ \text{Diameter} = 2 \times \text{Radius} = 2 \times 4 = 8 \text{ inches} \]
Therefore, the object formed is a **cone with a diameter of 8 inches**.
Since the base of the triangle has a length of 4 inches, when rotated, this leg serves as the radius of the base of the cone, which results in a diameter of:
\[ \text{Diameter} = 2 \times \text{Radius} = 2 \times 4 = 8 \text{ inches} \]
Therefore, the object formed is a **cone with a diameter of 8 inches**.
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