Question

The radius of the cone is 3 in and y = 5 in. What is the volume of the cone in terms of π?

Answer 1

Answer: The answer is A) 12π in^3

Answer 2

Answer:

  12π in³

Step-by-step explanation:

The right triangle formed by the radius (r), height (x), and slant height (y) is a 3-4-5 right triangle, with the dimension 4 inches being the perpendicular height from the base to the apex. That is, the Pythagorean theorem tells us ...

  r² + x² = y²

  x = √(y² -r²) = √(25 -9) = 4 . . . inches

The formula for the volume of a cone is ...

  V = (1/3)πr²h . . . . . . . . h is the height, what you call x

Your cone has r = 3 in, h = 4 in. Filling in these numbers and simplifying, we get ...

  V = (1/3)π(3 in)²(4 in) = 12π in³

The volume of the cone is 12π cubic inches.