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Find the volume of a right circular cone that has a height of
7.7cm and a base with a radius of
20cm. Round your answer to the nearest tenth of a cubic centimeter.
Answer:
cm^(3)

Find the volume of a right circular cone that has a height of $7.7 \mathrm{~cm}$ and a base with a radius of $20 \mathrm{~cm}$ . Round your answer to the nearest tenth of a cubic centimeter. $\newline$ Answer: $\mathrm{cm}^{3}$

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Convert between customary and metric systems

Full solution

Q. Find the volume of a right circular cone that has a height of

7.7 \mathrm{~cm}

and a base with a radius of

20 \mathrm{~cm}

. Round your answer to the nearest tenth of a cubic centimeter.

\newline

Answer:

\mathrm{cm}^{3}

Formula Explanation: To find the volume of a right circular cone, we use the formula: $\newline$ Volume = $(1/3) \cdot \pi \cdot r^2 \cdot h$ $\newline$ where $r$ is the radius of the base and $h$ is the height of the cone.
Given Values: First, we plug in the given values into the formula: $\newline$ Volume = $(\frac{1}{3}) \cdot \pi \cdot (20 \, \text{cm})^2 \cdot 7.7 \, \text{cm}$
Radius Calculation: Next, we calculate the square of the radius: $(20 \, \text{cm})^2 = 400 \, \text{cm}^2$
Substitution: Now we substitute the squared radius back into the volume formula: $\newline$ Volume = $(\frac{1}{3}) \cdot \pi \cdot 400 \, \text{cm}^2 \cdot 7.7 \, \text{cm}$
Multiplication: We perform the multiplication of the constants and the height: Volume = \left(\frac{\(1\)}{\(3\)}\right) \times \pi \times \(400 \, \text{cm}^ $2$ \times $7$ . $7$ \, \text{cm} = \left(\frac{ $1$ }{ $3$ }\right) \times \pi \times $3080$ \, \text{cm}^ $3$
Volume Calculation: We calculate the volume by multiplying the remaining terms: $\newline$ Volume $\approx \frac{1}{3} \times 3.14159 \times 3080 \, \text{cm}^3 \approx 1026.53 \times 3.14159 \, \text{cm}^3$
Approximation: Finally, we find the approximate value of the volume: $\text{Volume} \approx 3227.1847 \, \text{cm}^3$
Rounding: We round the volume to the nearest tenth of a cubic centimeter: $\text{Volume} \approx 3227.2\, \text{cm}^3$

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