Question

A sphere of ice cream is placed onto ice cream cone. Both have a diameter of 6cm. The height of your cone is 10cm. if you push the ice cream into the cone, will it fit. I answered ice cream volume 36 cone volume 30 but they were incorrect

Answer 1

Given that the ice-cream is in the shape of a sphere with diameter 6cm, so its volume is given by,

`\begin{gathered} V_i=(4)/(3)\pi R^3 \\ V_i=(4)/(3)\pi((d)/(2))^3 \\ V_i=(1)/(6)\pi(d)^3 \\ V_i=(1)/(6)\pi(6)^3 \\ V_i=36\pi \end{gathered}`

The ice-cre cone has a diameter 6 cm and height 10 cm, so its volume is calculated as,

`\begin{gathered} V_c=(1)/(3)\pi R^2h \\ V_c=(1)/(3)\pi((d)/(2))^2h \\ V_c=(1)/(12)\pi d^2h \\ V_c=(1)/(12)\pi(6)^2(10) \\ V_c=30\pi \end{gathered}`

Thus, the volume of ice-cream sphere is 36π cubic centimeters, and that of the corresponding cone is 30π cubic centimeters.

Note that the volume of the ice cream sphere is much larger than the volume of the cone.

Clearly, the whole ice-cream cannot fit inside the cone. So the answer is a NO.