Question

willa is making sandcastles with her little brother at the playground. they fill a cone - shaped bucket that has a diameter of 6 inches and a height of 10 inches with sand. what volume of sand can the cone - shaped bucket hold? 30π in.³ 90π in.³ 120π in.³ 60π in.³

Explanation:

Step1: Find the radius

Radius $r=\frac{d}{2}$, given $d = 6$ inches, so $r=\frac{6}{2}=3$ inches.

Step2: Use the cone - volume formula

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = 3$ inches and $h=10$ inches into the formula. $V=\frac{1}{3}\pi\times3^{2}\times10$.

Step3: Calculate the volume

First, $3^{2}=9$, then $\frac{1}{3}\times9\times10 = 3\times10=30$, so $V = 30\pi$ cubic inches.

Answer:

$30\pi$ in.$^{3}$