Volume of other 3D shapes (cylinders, cones, pyramids, spheres, etc)

Task goals

• Calculate the volume of a cylinder, cone, pyramid, or sphere from given dimensions, giving the answer in terms of $\pi$ where appropriate.
• Work backwards from a given volume to find an unknown radius, height, or base side length of a 3D shape.
• Solve real-world capacity problems involving cylindrical tanks, including answers rounded to a given number of decimal places and percentage-full scenarios.
• Compare the volumes of two solids that share a radius and height (e.g. explain why a cylinder's volume is three times a cone's), or find the total volume of a composite solid made from two joined shapes.
• Form and solve an algebraic equation to find an unknown dimension exactly when the volume is given in terms of $\pi$, such as after melting and recasting one solid into another.
• Investigate how the volume of a cylinder changes when its radius is doubled and its height is halved.