Question

Suppose a snow cone has a paper cone that is 8 centimeters deep and has a diameter of 5 centimeters. The flavored ice comes in a spherical scoop with a diameter of 5 centimeters and rests on top of the cone. If all the ice melts into the cone, will the cone overflow? Explain.

Answer 1

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.

$\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=2.5\\ h=8 \end{cases}\implies V=\cfrac{\pi (2.5)^2(8)}{3}\implies \implies \boxed{V=\cfrac{50\pi }{3}} \\\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad r=2.5\implies V=\cfrac{4(\pi )(2.5)^3}{3}\implies \boxed{V=\cfrac{125\pi }{6}} \\\\\\ \textit{the sphere's volume is larger, so yes, it will overflow}$

Answer 2

Answer:

Yes. The volume of the ice is greater than the volume of the cone.

Step-by-step explanation: