solve this---**Question Number:** 35
**Question Stem:**
A dairy farmer uses a storage silo that is in the shape of the right circular cylinder above. If the volume of the silo is 72π cubic yards, what is the diameter of the base of the cylinder, in yards?
**Diagram Description:**
* **Type:** Geometric figure (Diagram of a cylinder).
* **Main Elements:**
* **Shape:** Represents a right circular cylinder shown in perspective.
* **Lines:** Solid lines outline the visible sides and top ellipse. A dashed curve represents the hidden bottom ellipse. A dashed vertical line connects the center of the top base to the center of the bottom base, representing the axis of the cylinder.
* **Points:** A filled black circle is located at the center of the top base ellipse, and another filled black circle is located at the center of the bottom base ellipse.
* **Labels and Annotations:** A vertical double-headed arrow indicates the height of the cylinder on the right side. The height is labeled "8 yards".
* **Relative Position and Direction:** The diagram shows the cylinder standing upright. The height is indicated between the top and bottom bases.
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In this problem, we have a storage silo shaped like a right circular cylinder. We're told that the volume of the silo is 72 pi cubic yards, and the height is 8 yards. We need to find the diameter of the base of the cylinder.
To solve this problem, we'll use the formula for the volume of a cylinder. The volume equals pi times the square of the radius times the height. We substitute our known values: 72 pi equals pi times r squared times 8. Simplifying, we get 72 pi equals 8 pi r squared. Dividing both sides by 8 pi, we find that r squared equals 9, so the radius is 3 yards. Since the diameter is twice the radius, the diameter of the base is 6 yards.
To summarize what we've learned: The volume of a cylinder is pi times radius squared times height. When solving problems with cylinders, identify the known and unknown values, and rearrange the formula accordingly. Remember that the diameter is twice the radius. In our problem, with a volume of 72 pi cubic yards and height of 8 yards, we found the diameter to be 6 yards.
To solve this problem, we'll use the formula for the volume of a cylinder. The volume equals pi times the square of the radius times the height. We substitute our known values: 72 pi equals pi times r squared times 8. Simplifying, we get 72 pi equals 8 pi r squared. Dividing both sides by 8 pi, we find that r squared equals 9, so the radius is 3 yards. Since the diameter is twice the radius, the diameter of the base is 6 yards.
To summarize what we've learned: The volume of a cylinder is pi times radius squared times height. When solving problems with cylinders, identify the known and unknown values, and rearrange the formula accordingly. Remember that the diameter is twice the radius. In our problem, with a volume of 72 pi cubic yards and height of 8 yards, we found the diameter to be 6 yards.