Question

Hello! I need help in answering question number 3 which I will attach. Geometry 3 D shapes. It reads To make one order you need to fill the cone with ice cream first, and then add the scoop on top. How many total cubic inches of ice cream are in one order?

Answer 1

The ice-cream is made up of of a sugar cone and a scoop in the shape of half a sphere

Hence, the formula for the volume V of the total cubic inches of ice cream is:

`\begin{gathered} V\text{ = Volume of cone + half a volume of a sphere} \\ V\text{ = }(1)/(3)\pi r^2h\text{ + }(2)/(3)\pi r^3 \end{gathered}`

Given:

height of cone = 4.6 inches

radius of cone = 1.7 inches

radius of sphere = 1.7 inches

Substituting the given values:

`\begin{gathered} V\text{ = }(1)/(3)\text{ }*\text{ }\pi*\text{ 1.7}^2\text{ }*\text{ 4.6 + }(2)/(3)\text{ }*\text{ }\pi*\text{ 1.7}^3 \\ =\text{ 24.211 in}^3 \\ \approx\text{ 24.21 in}^3 \end{gathered}`

Answer:

24.21 cubic inches