Question

a party hat is shaped like a cone. the dimensions of the party hat are shown in the diagram. 9 in. 6 in. which measurement is closest to the volume of the party hat in cubic inches? 1,017.88 in³ 84.82 in³ 339.29 in³ 254.47 in³

Explanation:

Step1: Find radius of the cone

The diameter is 6 in, so radius $r = \frac{6}{2} = 3$ in.

Step2: Recall cone volume formula

The volume of a cone is $V = \frac{1}{3}\pi r^2 h$.

Step3: Substitute values and calculate

Substitute $r=3$, $h=9$, $\pi\approx3.1416$:

$$\begin{align*} V&=\frac{1}{3} \times 3.1416 \times 3^2 \times 9\\ &=\frac{1}{3} \times 3.1416 \times 9 \times 9\\ &=3.1416 \times 3 \times 9\\ &=3.1416 \times 27\\ &\approx 84.82 \end{align*}$$

Answer:

84.82 $in^3$ (Option: 84.82 $in^3$)