Neco 2021 Mathematics Question 13

Practice essay / theory question 13 from the 2021 Neco Mathematics examination. This question covers mensuration, volume, surface area, composite solids .

Neco 2021 Mathematics Essay / Theory
Topics: mensuration volume surface area composite solids
Question 13 NECO • 2021 • MATHEMATICS • essay
Neco 2021 Mathematics Question 13 diagram

A solid is formed as follows: - A right circular cylinder of radius \(5\) cm and height \(12\) cm. - A hemisphere of radius \(5\) cm is attached to the base of the cylinder (the circular base of the cylinder is completely covered by the hemisphere). - From the top of the cylinder a right circular cone of radius \(5\) cm and height \(8\) cm is removed, the base of the cone coinciding with the top circular face of the cylinder. The resulting solid has a cylindrical body, a hemispherical extension at the bottom and a conical cavity at the top. Answer the following questions:

Question Parts

( a )
Find the total surface area of the solid, including all exposed curved surfaces. Give your answer in terms of \(\pi\) and simplify where possible.
( b )
Determine the volume of the solid. Express your answer as a multiple of \(\pi\).
( c )
If the solid is painted on all its exposed surfaces and then completely immersed in water, calculate the ratio of the volume of water displaced (in \(\text{cm}^3\)) to the total painted surface area (in \(\text{cm}^2\)). Express the ratio in its simplest exact form and also give a decimal approximation to three decimal places.

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About This Question

This is Neco 2021 Mathematics Question 13. It is one of the essay questions from the 2021 Neco Mathematics examination.

The question covers mensuration, volume, surface area, composite solids .

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