Question

if a cone has a radius of 5 cm and a height of 10 cm, its volume is: a. 250π cm³ b. 50/3 π cm³ c. 250/3 π cm³ d. 25π cm³ if the height of a cone is doubled and the radius remains the same, the new volume will be: a. doubled b. halved c. tripled d. unchanged

Explanation:

Step1: Recall the volume formula of a cone

The volume formula of a cone is \( V=\frac{1}{3}\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height.

Step2: Substitute \( r = 5\) and \( h = 10\) into the formula

\( V=\frac{1}{3}\pi\times5^{2}\times10=\frac{1}{3}\pi\times25\times10=\frac{250}{3}\pi\ \text{cm}^{3} \)

Step3: Analyze the effect of doubling the height

Let the original volume be \( V_{1}=\frac{1}{3}\pi r^{2}h \). When the height is doubled (\( h_{2} = 2h \)), the new volume \( V_{2}=\frac{1}{3}\pi r^{2}(2h)=2\times(\frac{1}{3}\pi r^{2}h)=2V_{1} \)

Answer:

For the first question: C. \( \frac{250}{3}\pi\ \text{cm}^{3} \)
For the second question: A. Doubled