To find the volume of the first cylindric ice cream. Its height is 8 centimeters and its diameter is 4 centimeters. Let's use the formula for the volume of a cylinder.
[tex]V_{\text{cylinder}}=\pi(r)^2h[/tex]
Replacing the given information, we have.
[tex]V_{\text{cylinder}}=3.14(2)^2\cdot8=3.14\cdot4\cdot8=100.5\operatorname{cm}[/tex]
On the other hand, we use the circular cone formula to find the volume of the second ice cream.
[tex]V_{\text{cone}}=\frac{1}{3}\pi(r)^2h[/tex]
Let's replace the given information.
[tex]V_{\text{cone}}=\frac{1}{3}\cdot3.14\cdot(2)^2\cdot11.5=48.11\operatorname{cm}[/tex]
Then, we subtract the volumes.
[tex]\Delta V=100.5-48.1\approx52.4\operatorname{cm}^3[/tex]
Hence, the answer is C.
