Question

determine the number of cubic centimeters of ice cream that you have in the cone and the scoop on top

Answer 1

Given a cone and a scoop of ice cream.

To determine: The cubic centimeters of ice cream

Solution:

The ice is a combination of the shape of a cone and a hemisphere. To find the cubic centimeters of the ice cream, we would find the volume of the cone and the hemisphere.

$V_{\text{ice cream}}=V_{cone}+V_{hemisphere}$$\begin{gathered} V_{\text{cone}}=\frac{1}{3}\pi r^2h \\ d=6\operatorname{cm}(given) \\ r=\frac{d}{2}=\frac{6\operatorname{cm}}{2}=3\operatorname{cm} \\ h=13\operatorname{cm}(\text{given)} \end{gathered}$$\begin{gathered} V_{\text{cone}}=\frac{1}{3}\pi r^2h \\ V_{\text{cone}}=\frac{1}{3}\pi\times3^2\times13 \\ V_{\text{cone}}=39\pi\operatorname{cm}^3 \end{gathered}$$\begin{gathered} V_{\text{hemisphere}}=\frac{2}{3}\pi r^3 \\ r=3\operatorname{cm} \\ V_{\text{hemisphere}}=\frac{2}{3}\pi\times3^3 \\ V_{\text{hemisphere}}=18\pi cm^3 \end{gathered}$$\begin{gathered} V_{\text{ice cream}}=V_{cone}+V_{hemisphere} \\ V_{\text{ice cream}}=39\pi cm^3+18\pi cm^3 \\ V_{\text{ice cream}}=57\pi cm^3 \\ V_{\text{ice cream}}=179.07\operatorname{cm}^3 \end{gathered}$

Hence, the number of cubic centimeters of ice cream is 179.07cm³