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${:[1.5^(2)n*h=67quad(h=9.48" in "],[(7.0 n)/(7.07)=(67)/(207)=9.48]:} ceam cone is filled with a volume of 230in^(3) of ice cream, which includes the ice cream in the cone rounded scoop on top, as shown. What is the volume of just the cone? Round to the nearest whole 280 r^(2)pi (3.5^(2)pi*h)/(3)=230 3.5 3.5 1743$

$\begin{array}{l} 1.5^{2} n \cdot h=67 \quad(h=9.48 \text { in } \\ \frac{7.0 n}{7.07}=\frac{67}{207}=9.48 \end{array}$ $\newline$ ceam cone is filled with a volume of $230 \mathrm{in}^{3}$ of ice cream, which includes the ice cream in the cone rounded scoop on top, as shown. What is the volume of just the cone? Round to the nearest whole $280$ $\newline$ $r^{2} \pi$ $\newline$ $\frac{3.5^{2} \pi \cdot h}{3}=230$ $\newline$ $3$ . $5$ $\newline$ $3$ . $5$ $\newline$ $1743$

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\begin{array}{l} 1.5^{2} n \cdot h=67 \quad(h=9.48 \text { in } \\ \frac{7.0 n}{7.07}=\frac{67}{207}=9.48 \end{array}

\newline

ceam cone is filled with a volume of

230 \mathrm{in}^{3}

of ice cream, which includes the ice cream in the cone rounded scoop on top, as shown. What is the volume of just the cone? Round to the nearest whole

280

\newline

r^{2} \pi

\newline

\frac{3.5^{2} \pi \cdot h}{3}=230

\newline

3

5

\newline

3

5

\newline

1743

Write Formula for Volume: First, let's write down the formula for the volume of a cone, which is $V = \frac{1}{3}\pi r^2 h$ .
Find Volume of Cone: We know the total volume of ice cream including the cone and the scoop is $230 \, \text{in}^3$ . We need to find the volume of just the cone.
Plug in Value of h: The formula given is $(3.5^2\pi h)/3 = 230$ . Let's plug in the value of h, which is $9.48$ inches.
Calculate Left Side: Now, calculate the left side of the equation: $(3.5^2\pi\times9.48)/3$ .
Perform Multiplication: Perform the calculation: $(3.5^2 \times \pi \times 9.48) / 3 = (12.25 \times \pi \times 9.48) / 3$ .
Divide by $3$ : Calculate the multiplication: $12.25 \times \pi \times 9.48 \approx 364.17\pi$ .
Compare to Total Volume: Now, divide by $3$ : $364.17\pi / 3 \approx 121.39\pi$ .
Correct Previous Calculation: Finally, we compare this result to the total volume of $230 \, \text{in}^3$ to find the volume of the scoop. But wait, we made a mistake in the previous step, we should have divided $364.17\pi$ by $3$ before comparing it to $230 \, \text{in}^3$ .