Question

1. a cone - shaped cup has a height of 8 cm and a radius of 3 cm. what is the volume of liquid it can hold?

a. (24pimathrm{cm}^{3})
b. (11pimathrm{cm}^{3})
c. (16pimathrm{cm}^{3})
d. (72pimathrm{cm}^{3})

Explanation:

Step1: Recall the volume formula for a cone

The volume formula for a cone is \(V=\frac{1}{3}\pi r^{2}h\), where \(r\) is the radius and \(h\) is the height.

Step2: Substitute the given values into the formula

Given \(r = 3\mathrm{cm}\) and \(h=8\mathrm{cm}\), substitute into \(V=\frac{1}{3}\pi r^{2}h\). So \(V=\frac{1}{3}\pi\times(3)^{2}\times8\).

Step3: Simplify the expression

First, calculate \((3)^{2}=9\). Then \(\frac{1}{3}\times9\times8 = 3\times8=24\). So \(V = 24\pi\mathrm{cm}^3\).

Answer:

A. \(24\pi\mathrm{cm}^3\)