Question

milo 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 120π in.³ 30π in.³ 90π in.³

Explanation:

Step1: 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.

Step2: Find the radius

The diameter of the cone - shaped bucket is 6 inches. The radius \( r \) is half of the diameter, so \( r=\frac{6}{2}=3 \) inches. The height \( h = 10 \) inches.

Step3: Substitute the values into the formula

Substitute \( r = 3 \) and \( h = 10 \) into the volume formula:

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If we take \( \pi\approx3.14 \), then \( V = 30\times3.14=94.2 \) (but the option with \( 30\pi \) is also a valid expression for the volume).

Answer:

\( 30\pi\space in^3 \) (assuming the first option is \( 30\pi\space in^3 \))