Answer: ![159.2\ cm^3](https://tex.z-dn.net/?f=159.2%5C%20cm%5E3)
Step-by-step explanation:
The volume of cone is given by :-
![\text{Volume}=\frac{1}{3}\pi r^2h](https://tex.z-dn.net/?f=%5Ctext%7BVolume%7D%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2h)
Given: The diameter of paper cups = 8 cm
Thus, the radius of paper cup (r)=![\frac{8}{2}=4\ cm](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B2%7D%3D4%5C%20cm)
The height of paper cup (h)= 9.5 cm
Now, the volume of paper cup will be :-
![\text{Volume}=\frac{1}{3}\pi (4)^2(9.5)\\\\\Rightarrow\text{Volume}=\frac{1}{3}(3.14159265359)\times(16)(9.5)=159.174027782\approx159.3\ cm^3](https://tex.z-dn.net/?f=%5Ctext%7BVolume%7D%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%284%29%5E2%289.5%29%5C%5C%5C%5C%5CRightarrow%5Ctext%7BVolume%7D%3D%5Cfrac%7B1%7D%7B3%7D%283.14159265359%29%5Ctimes%2816%29%289.5%29%3D159.174027782%5Capprox159.3%5C%20cm%5E3)
Hence, the best approximation for the volume of the paper cup ![159.2\ cm^3](https://tex.z-dn.net/?f=159.2%5C%20cm%5E3)