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? 120π in.³ 30π in.³ 90π in.³ 60π in.³

Explanation:

Step1: Find the radius of the cone

The diameter of the cone is 6 inches, so the radius \( r=\frac{d}{2}=\frac{6}{2} = 3 \) inches.

Step2: Recall the formula for the volume of a cone

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

Step3: Substitute the values of \( r \) and \( h \) into the formula

We know \( r = 3 \) inches and \( h=10 \) inches. Substituting these values, we get:
\( V=\frac{1}{3}\pi\times(3)^{2}\times10 \)
First, calculate \( (3)^{2}=9 \). Then,
\( V=\frac{1}{3}\pi\times9\times10 \)
\( \frac{1}{3}\times9 = 3 \), so \( V = 3\times10\times\pi=30\pi \) cubic inches.

Answer:

\( 30\pi \text{ in.}^3 \) (corresponding to the option "30π in.³")