Final answer:
The radius of the double cone formed by revolving the right triangle with legs of 6 cm and 8 cm around its hypotenuse is 6 cm. This radius is equal to the length of the shorter leg of the triangle.
Step-by-step explanation:
The student has asked to find the radius of the double cone formed by revolving a right triangle around its hypotenuse. To solve this problem, we must first find the length of the hypotenuse using the Pythagorean theorem, which states that in a right triangle with legs of length a and b, and hypotenuse c, the relationship is c = √(a² + b²). In this case, the legs are 6 cm and 8 cm.
Applying the formula:
- c = √(6² + 8²)
- c = √(36 + 64)
- c = √100
- c = 10 cm
Since the right triangle is revolved around its hypotenuse to form the double cone, the radius of each cone will be equal to the length of the shorter leg of the triangle, which is 6 cm.