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Volumes of Standard Solids

Volumes of cylinders. r. Volumes of Standard Solids. h. h. r. Volumes of pyramids and cones. L. Volumes of spheres. r. Volumes of prisms. A. Try some Unit test level questions. Volume of a cylinder. The formula for the volume of a cylinder is.

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Volumes of Standard Solids

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  1. Volumes of cylinders r Volumes of Standard Solids h h r Volumes of pyramids and cones L Volumes of spheres r Volumes of prisms A Try some Unit test level questions

  2. Volume of a cylinder The formula for the volume of a cylinder is Where r is the radius of the circular end and h is the height of the cylinder. As usual,  can be approximated by 3.14 You should set out your working in the standard way: Formula, Substitution, Calculation then Rounding (if needed). For example, calculate the volume of a cylinder with radius 25cm and height 60cm giving your answer to 3 significant figures. For better readability, arrange each step like this by lining up the equals signs in a column

  3. Volume of a Sphere The formula for the volume of a sphere is Where r is the radius of the sphere. As usual,  can be approximated by 3.14 You should set out your working in the standard way: Formula, Substitution, Calculation then Rounding if needed. For example, calculate the volume of a sphere of radius 37 mm. Roundyour answer to 2 significant figures. Don’t round answers as you go along. Do the whole calculation and THEN do the rounding

  4. Volume of a prism Remember, a Prism is an object with a constant cross section like a cylinder or a cuboid.The simple formula for the volume of a prism is: Where A is the area of the constant cross-section and h is the height (or length) of the prism Example: Calculate the volume of a prism of cross-sectional area 75cm2 and length 150cm You may have to use your knowledge of 2D shapes to calculate the end Area, A, yourself.

  5. Volume of a Cone or Pyramid The formula for the volume of a cone is Where r is the radius of the circular base and h is the perpendicular height. As usual,  can be approximated by 3.14 The Volume of a pyramid is very similar: it is V = ⅓ A h where A is the area of the base. In the cone formula, the base is a circle and A is replaced with r2. Example, calculate the volume of a cone of radius 11 cm, and height 14cm. Round your answer to 2 significant figures.

  6. Unit Assessment Volume questions This is an example of the problem-solving style of question that you can also expect in the Unit assessment The examples on the earlier slides for cone, sphere and cylinder cover the level of question that you can expect for one or two of the unit assessment questions. These are very routine questions and they are very easy to prepare for – make sure that you do. A toy manufacturer stores liquid resin in cylindrical cans of radius 35 cm and height 50 cm.a) Calculate the volume of the cylinder. They use the resin to make spherical balls of radius 5 cm.b) Calculate the volume of a single ball. c) How many balls can be made from one completely full can? a) b) c) The number of balls that can be made is This means that they can make 367 balls.

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