Question

what is the volume of the cone? cone $v = \frac{1}{3}bh$ $\frac{490}{3}\pi cm^{3}$ $\frac{700}{3}\pi cm^{3}$ $\frac{140}{3}\pi cm^{3}$ $\frac{70}{3}\pi cm^{3}$

Explanation:

Step1: Find the base area \( B \)

The base of the cone is a circle. The formula for the area of a circle is \( B=\pi r^{2} \), where \( r = 7\mathrm{cm} \).
So, \( B=\pi\times(7)^{2}=49\pi\mathrm{cm}^{2} \).

Step2: Substitute into the volume formula

The volume formula for a cone is \( V=\frac{1}{3}Bh \). Here, \( B = 49\pi\mathrm{cm}^{2} \) and \( h=10\mathrm{cm} \).
Substitute these values: \( V=\frac{1}{3}\times49\pi\times10=\frac{490}{3}\pi\mathrm{cm}^{3} \).

Answer:

\(\frac{490}{3}\pi\mathrm{cm}^{3}\)