Volume of cylinders
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This document discusses the formula for calculating the volume of cylinders. It begins by reviewing the formulas for finding the volume of 3D objects like cubes. It then defines key terms like volume and the units used to measure it. The main formula presented is that the volume of a cylinder equals the area of the circular base multiplied by the height. The area of the circular base is calculated using pi r squared. An example problem demonstrates how to find the volume of a cylinder with a given radius and height by using this formula. In the end, it summarizes that the volume of a prism or cylinder is calculated as the area of the base multiplied by the height.
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This document provides instruction on calculating the volumes of cylinders, cones, and spheres. It defines key terms like radius, height, volume, and presents the formulas. For cylinders, the volume formula is given as V = πr^2h. For cones, the formula is the same as cylinders but divided by 1/3. For spheres, the volume formula is V = 4/3πr^3. Examples are shown for each shape calculating volumes when given the radius and height. In the summaries, the learner reflects on what they've learned about each shape's volume formula and if they can answer the lesson's essential question.
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This document provides information about calculating the surface area and volume of spheres. It begins with examples of finding the volume and surface area of spheres using the formulas V=4/3πr^3 and S=4πr^2. It then discusses how changing the radius affects volume and surface area. The document concludes with examples of finding the surface area and volume of composite figures made of spheres, cylinders, and hemispheres.
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Pythagoras' Theorem allows you to calculate the lengths of sides in a right-angled triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be used to find missing side lengths or to determine if a triangle is right-angled. It is commonly applied to problems involving distances, lengths, and geometrical shapes containing right triangles.
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Volume of cylinders
- 1. VOLUME OF CYLINDERS Lesson One: End of Year Acceleration 2013
- 2. WARM-UP Find the volume of the following 3D objects. A cube with sides of 5.5 cm. The object below: 166.38 cm3 3,412.5 in3 15 in 17.5 in 13 in MCC8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
- 3. RECAP OF WARM-UP What formula did you use to find the volume of the 3D objects? L x W x H L x W = Area of the base figure MCC8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
- 4. PARTS OF A CYLINDER Sketch a cylinder and label the radius and height.
- 5. VOLUME Volume – Is the space that a figure occupies. Remember it is measured in cubic units. cm3, in3, m3, ft3 MCC8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
- 6. II. VOLUME OF A CYLINDER r h V = Bh Volume of right cylinder Height of cylinder Area of base: (Circle) A = r2 MCC8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
- 7. 16ft 9ft V = Bh = r2 • h = (8ft)2 • (9ft) = 64ft2 • (9ft) = 576ft3 = 1809.6ft3 Area of a Circle MCC8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
- 8. WHAT HAVE WE LEARNED?? Volume of a prism or a cylinder: V = Bh Capitol “B” stands for area of the base. Composite Figures: Made up of two separate solids. MCC8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.