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Mensuration (Pyramid, Cones and Spheres) - Volume and Surface Area of Composite Solids

Mensuration (Pyramid, Cones and Spheres) - Volume and Surface Area of Composite Solids

IP 2

The diagram below shows a cone of radius \(7\) cm with a hemisphere cut out of it. Given that the slant height of the cone is \(14\) cm and the shaded area of the base is \(40\pi\) \(\text{cm}^2\), find

  1. the radius of the hemisphere \(OD\),
  2. the volume of the object,
  3. the surface area of the object.

Solution:

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Answer:(a) \(3\text{ cm}\); (b) \(\left(\frac{343\sqrt3}{3}-18\right)\pi\text{ cm}^3\approx566\text{ cm}^3\); (c) \(156\pi\text{ cm}^2\approx490\text{ cm}^2\) (3 s.f.).

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