Calculate the area and the volume of the cone.
Understand the Problem
The image shows a cone with a height of 6.7 feet and a diameter of 8.8 feet. Presumably the question is asking to calculate some values of the cone, but the image does not contain the question so I cannot complete the request.
Answer
$V \approx 135.97$ cubic feet.
Answer for screen readers
The volume of the cone is approximately $135.97$ cubic feet.
Steps to Solve
- Find the radius of the cone
The diameter is given as 8.8 ft. The radius $r$ is half of the diameter. $r = \frac{8.8}{2} = 4.4$ ft
- Calculate the area of the base
The base of the cone is a circle. The area $A$ of a circle is given by $A = \pi r^2$
Substituting the value of $r$: $A = \pi (4.4)^2 = \pi (19.36) \approx 60.88$ square feet.
- Calculate the volume of the cone
The volume $V$ of a cone is given by $V = \frac{1}{3}Ah$, where A is the base area and h is the height.
Substituting the values of $A$ and $h$: $V = \frac{1}{3} \times 60.88 \times 6.7 \approx \frac{1}{3} \times 407.896 \approx 135.97$ cubic feet.
The volume of the cone is approximately $135.97$ cubic feet.
More Information
The volume of the cone is significantly less than the value of 474.7 shown in the original image. It's possible that this value refers to a different shape but without more context, it's hard to know for sure.
Tips
A common mistake is forgetting to divide the diameter by 2 to get the radius when calculating the area of the base. Another common mistake is using the formula for the volume of a cylinder instead of the volume of a cone.
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