Question
What is the volume, in cubic inches, of a cone with a diameter of 6 inches and a height of 7 inches? Round your answer to the nearest hundredth. (1 point) cubic inches
Answers
Answered by
GPT-4 Turbo
To find the volume \( V \) of a cone, you can use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height of the cone. Given that the diameter of the cone is 6 inches, the radius \( r \) is half of that, which is 3 inches. The height \( h \) is given as 7 inches.
Now plug the values into the formula:
\[ V = \frac{1}{3} \pi (3)^2 (7) \]
\[ V = \frac{1}{3} \pi (9) (7) \]
\[ V = 3 \pi (7) \]
\[ V = 21 \pi \]
Since \( \pi \) is approximately 3.14159, the volume can be calculated as:
\[ V \approx 21 \times 3.14159 \]
\[ V \approx 65.97342 \text{ cubic inches} \]
Rounded to the nearest hundredth, the volume of the cone is approximately 65.97 cubic inches.
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height of the cone. Given that the diameter of the cone is 6 inches, the radius \( r \) is half of that, which is 3 inches. The height \( h \) is given as 7 inches.
Now plug the values into the formula:
\[ V = \frac{1}{3} \pi (3)^2 (7) \]
\[ V = \frac{1}{3} \pi (9) (7) \]
\[ V = 3 \pi (7) \]
\[ V = 21 \pi \]
Since \( \pi \) is approximately 3.14159, the volume can be calculated as:
\[ V \approx 21 \times 3.14159 \]
\[ V \approx 65.97342 \text{ cubic inches} \]
Rounded to the nearest hundredth, the volume of the cone is approximately 65.97 cubic inches.
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