4. Five marks exercise problems I

1. A vessel is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter is \(14 \ cm\) and the height of the vessel is \(13 \ cm\). Find the capacity of the vessel.

 

Answer:

 

The capacity of the vessel \(=\)  \(cm^3\)

 

2. Nathan, an engineering student was asked to make a model shaped like a cylinder with two cones attached at its two ends. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of the model that Nathan made.

 

Answer:

 

The volume of the model \(=\)  \(cm^3\)

 

 

3. From a solid cylinder whose height is \(2.4 \ cm\) and the diameter \(1.4 \ cm\), a cone of the same height and same diameter is carved out. Find the volume of the remaining solid to the nearest \(cm^3\).

 

Answer:

 

The volume of the remaining solid \(=\)  \(cm^3\)

 

[Note: Round off your answer to two decimal places.]