Question

The volume of a cone is \( 1570 \, cm^3 \). If the area of its base is \( 314 \, cm^2 \), then its height is:

• A. \( 10 \, cm \)
• B. \( 15 \, cm \)
• C. \( 18 \, cm \)
• D. \( 20 \, cm \)

Hint:

The height of a cone can be found using \( h = \frac{3V}{\pi r^2} \) when the base area is given directly as \( \pi r^2 \).

Answer 1

The Correct Option is B

Step 1: Identify the formula The volume of a cone is given by: \[ V = \frac{1}{3} \pi r^2 h \] where: - \( V = 1570 \, cm^3 \) (given volume), - \( \pi r^2 = 314 \, cm^2 \) (given base area). Step 2: Solve for height Rearrange the formula: \[ h = \frac{3V}{\pi r^2} \] Substituting values: \[ h = \frac{3 \times 1570}{314} \] \[ h = \frac{4710}{314} = 15 \text{ cm} \] Step 3: Conclusion Thus, the correct height of the cone is \( 15 \, cm \).