Answer :
1. Find the radius: The diameter is given as 5 cm, so to find the radius (r), we divide the diameter by 2: r = 5 cm / 2 = 2.5 cm.
2. Plug in the values: Now that we have the radius (r) and the height (h), we can plug them into the formula for the volume of a cone: V = (1/3)πr²h.
3. Calculate: Substitute the values into the formula:
V = (1/3)π(2.5 cm)²(12 cm).
4. Square the radius: Calculate the square of the radius: (2.5 cm)² = 6.25 cm².
5. Multiply: Now multiply the squared radius by the height and by π, and then divide by 3:
V = (1/3)π(6.25 cm²)(12 cm).
6. Calculate the result: Multiply 6.25 by 12, then multiply by π, and finally divide by 3:
V ≈ (1/3)π(75 cm³) ≈ 78.54 cm³.
So, the volume of the cone is approximately 78.54 cubic centimeters.
