Answer:
V = 96π cm³
Step-by-step explanation:
The formula of a volume of a cone:
[tex]V=\dfrac{1}{3}\pi r^2H[/tex]
We have r = 6cm and l = 10cm.
Use the Pythagorean theorem to calculate the height H:
[tex]H^2+r^2=l^2[/tex]
Substitute:
[tex]H^2+6^2=10^2[/tex]
[tex]H^2+36=100[/tex] subtract 36 from both sides
[tex]H^2=64\to H=\sqrt{64}\\\\H=8\ cm[/tex]
Calculate the volume:
[tex]V=\dfrac{1}{3}\pi(6^2)(8)=\dfrac{1}{3}\pi(36)(8)=\pi(12)(8)=96\pi\ cm^3[/tex]
