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1.In what way does a cylinder resemble the shape of a prism? 2.How are the formulas for the volumes of prisms and cylinders similar and different? 3.What do the formulas look like for the volumes of a prism and cylinder? 4.How many collection barrels does the gardener need? : Volumes of Cylinders, Pyramids, and Cones
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A gardener in Texas is designing a rainwater collection system. She will collect rainwater from her roof to water her garden. The collection barrels are cylinders that are 1.3 meters high and have a radius of 40 cm. A cylinder is a solid or hollow object that has two parallel bases connected by a curved surface. The gardener wants to collect at least 5 cubic meters of water.
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3.5.2: Volumes of Cylinders, Pyramids, and Cones
1. In what way does a cylinder resemble the shape of a prism?
2. How are the formulas for the volumes of prisms and cylinders similar and different?
3. What do the formulas look like for the volumes of a prism and cylinder?
4. How many collection barrels does the gardener need?
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3.5.2: Volumes of Cylinders, Pyramids, and Cones
1. In what way does a cylinder resemble the shape of a prism? • Both are three-dimensional objects. Both have a
height and two parallel bases.
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3.5.2: Volumes of Cylinders, Pyramids, and Cones
2. How are the formulas for the volumes of prisms and cylinders similar and different? • Since a cylinder resembles a prism in some ways,
the volume formulas are similar. They are similar in that the basic premise of each formula is to multiply the area of the base times the height. They are different because the areas of the bases are calculated differently. While the prism base is length • width, the base of the cylinder is r 2.
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3.5.2: Volumes of Cylinders, Pyramids, and Cones
3. What do the formulas look like for the volumes of a prism and cylinder?• The circle at the base of a cylinder has an area
formula of A = r 2.• If you multiply the area of the cylinder’s base times
the height, the formula for the volume of a cylinder would be as follows:
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3.5.2: Volumes of Cylinders, Pyramids, and Cones
4. How many collection barrels does the gardener need? • The radius of a barrel is 40 cm. Convert this to
meters.
• The radius of the barrel is 0.4 meters.
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3.5.2: Volumes of Cylinders, Pyramids, and Cones
The height of the barrel is 1.3 meters. Substitute these dimensions into the formula.
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3.5.2: Volumes of Cylinders, Pyramids, and Cones
Formula for volume of a cylinderSubstitute known dimensions of the water barrel.
• One barrel will hold approximately 0.6534 cubic meters of water. The gardener wants to collect at least 5 cubic meters of water. Therefore, divide 5 by 0.6534 to determine the number of needed barrels.
• Since the gardener can’t have 0.65 of a barrel, round up to 8 barrels.
• The gardener needs 8 water barrels to collect at least 5 cubic meters of water.
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3.5.2: Volumes of Cylinders, Pyramids, and Cones
