Final answer:
The slant height H of the cone is found using the Pythagorean theorem. By plugging in the given radius of 3 inches and height of 4 inches, we calculate that H equals 5 inches, so the correct answer is option b) H = 5 inches.
Step-by-step explanation:
The student's question involves finding the slant height H of a cone with a given radius and height. Specifically, the cone has a radius of 3 inches and a height of 4 inches. To find the slant height H, we can use the Pythagorean theorem since the radius, height, and slant height form a right triangle. The formula for the slant height H in a right triangle is H = √(r² + h²), where r is the radius and h is the height of the cone.
Applying the formula:
- H = √(3² + 4²)
- H = √(9 + 16)
- H = √25
- H = 5 inches
Thus, the correct answer is b) H = 5 inches.