check the picture below.
so the cone itself has a height of 8, and a radius of 2.5, and the spherical scoop, ready to melt in it, has a radius of 2.5.
namely, will the volume of the sphere be larger than the cone? in which case the melted ice-cream will overflow.
[tex] \bf \textit{volume of a cone}\\\\
V=\cfrac{\pi r^2 h}{3}~~
\begin{cases}
r=2.5\\
h=8
\end{cases}\implies V=\cfrac{\pi (2.5)^2(8)}{3}\implies \implies \boxed{V=\cfrac{50\pi }{3}}
\\\\\\
\textit{volume of a sphere}\\\\
V=\cfrac{4\pi r^3}{3}\qquad r=2.5\implies V=\cfrac{4(\pi )(2.5)^3}{3}\implies \boxed{V=\cfrac{125\pi }{6}}
\\\\\\
\textit{the sphere's volume is larger, so yes, it will overflow} [/tex]
Answer:
Yes. The volume of the ice is greater than the volume of the cone.
Step-by-step explanation:
