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Cone- volume: 36 cubic inches; height: 9 inches. Find the radius to the nearest whole

Cone- volume: $36$ cubic inches; height: $9$ inches. Find the radius to the nearest whole

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Circles: word problems

Full solution

Q. Cone- volume:

36

cubic inches; height:

9

inches. Find the radius to the nearest whole

Use Cone Volume Formula: We will use the formula for the volume of a cone, which is $V = \frac{1}{3} \pi r^2 h$ , where $V$ is the volume, $r$ is the radius, and $h$ is the height. $\newline$ Given: Volume $V = 36$ cubic inches, Height $h = 9$ inches. $\newline$ We need to solve for $r$ .
Rearrange Formula for r^ $2$ : First, we rearrange the formula to solve for $r^2$ : $\newline$ $r^2 = \frac{3V}{\pi h}$ .
Plug in Given Values: Next, we plug in the given values for $V$ and $h$ into the rearranged formula: $\newline$ $r^2 = \frac{3 \times 36}{\pi \times 9}$ .
Calculate Value Inside Fraction: We calculate the value inside the fraction: $\newline$ $r^2 = \frac{108}{\pi \times 9}$ .
Simplify Fraction: We simplify the fraction by dividing $108$ by $9$ : $\newline$ $r^2 = \frac{12}{\pi}$ .
Approximate pi and Divide: We approximate $\pi$ as $3$ . $14$ and divide $12$ by $3$ . $14$ to find $r^2$ : $\newline$ $r^2 = \frac{12}{3.14}$ .
Perform Division: We perform the division: $\newline$ $r^2 \approx 3.82$ .
Find r by Taking Square Root: To find $r$ , we take the square root of $r^2$ : $\newline$ $r \approx \sqrt{3.82}$ .
Calculate Square Root: We calculate the square root of $3$ . $82$ : $\newline$ $r \approx 1.95$ .
Round to Nearest Whole Number: Since we need to round to the nearest whole number, we round $1.95$ to $2$ .

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