Question

1. an ice cream cone is topped with one hemispherical scoop of chocolate ice cream as shown below. note that the diagram is not drawn to scale. the diameter of the scoop of ice cream, which matches the diameter of the widest part of the cone, is 6 cm. the vertical height of the cone is 10 cm. what expression can be used to calculate the volume of this entire object (cone + hemisphere of ice cream)? 33) state the value of each of the angles in the following diagrams:

Explanation:

Step1: Find the volume of the cone

The formula for the volume of a cone is \(V_{cone}=\frac{1}{3}\pi r^{2}h\). Given that the diameter \(d = 6\mathrm{cm}\), so the radius \(r=\frac{d}{2}=3\mathrm{cm}\) and the height \(h = 10\mathrm{cm}\).
Substitute into the formula: \(V_{cone}=\frac{1}{3}\pi\times(3)^{2}\times10=\frac{1}{3}\pi\times9\times 10 = 30\pi\mathrm{cm}^{3}\)

Step2: Find the volume of the hemisphere

The formula for the volume of a hemisphere is \(V_{hemisphere}=\frac{2}{3}\pi r^{3}\). Since \(r = 3\mathrm{cm}\)
Substitute into the formula: \(V_{hemisphere}=\frac{2}{3}\pi\times(3)^{3}=\frac{2}{3}\pi\times27=18\pi\mathrm{cm}^{3}\)

Step3: Find the total volume

The total volume \(V = V_{cone}+V_{hemisphere}\)
\(V=(30\pi + 18\pi)\mathrm{cm}^{3}=48\pi\mathrm{cm}^{3}\)

Answer:

The expression \(\frac{1}{3}\pi\times3^{2}\times10+\frac{2}{3}\pi\times3^{3}\) (or \(48\pi\)) can be used to calculate the volume of the entire object.