5. Five marks exercise problems II

1. A solid consisting of a right circular cone of height \(12 \ cm\) and radius \(6 \ cm\) standing on a hemisphere of radius \(6 \ cm\) is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of the water displaced out of the cylinder, if the radius of the cylinder is \(6 \ cm\) and height is \(18 \ cm\).

 

 

Answer:

 

The volume of the water displaced out of the cylinder \(=\)  \(cm^2\)

 

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

 

 

2. A capsule is in the shape of a cylinder with two hemisphere stuck to each of its ends. If the length of the entire capsule is \(12 \ mm\) and the diameter of the capsule is \(3 \ mm\), how much medicine it can hold?

 

Answer:

 

The capsule can hold  \(cm^2\) of medicine.

 

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

 

 

3. As shown in figure a cubical block of side \(7 \ cm\) is surmounted by a hemisphere. Find the surface area of the solid.

 

 

Answer:

 

The surface area of the solid \(=\)  \(cm^2\)

 

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