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:

For cones, the volume formula is: \[ V = \frac{1}{3} \pi r^2 h \] To find height: \[ h = \frac{3V}{\pi r^2} \]

Answer 1

The Correct Option is A

The volume of a cone is given by:
\[ V = \frac{1}{3} \pi r^2 h \] Given: \[ V = 1570, \quad \text{Base Area} = \pi r^2 = 314 \] Rewriting the formula: \[ h = \frac{3V}{\pi r^2} \] Substituting values: \[ h = \frac{3(1570)}{314} \] \[ h = \frac{4710}{314} = 10 \text{ cm} \]