5. Five marks exercise problems II

1. Seenu’s house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (underground tank) which is in the shape of a cuboid. The sump has dimensions \(2 \ m\) \(\times\) \(1.5 \ m\) \(\times\) \(1 \ m\). The overhead tank has its radius of \(60 \ cm\) and height \(105 \ cm\). Find the volume of the water left in the sump after the overhead tank has been completely filled with water from the sump which has been full, initially.

 

Answer:

 

Volume of the water left in the sump \(=\)  \(m^3\)

 

[Note: Enter your answer up to three decimal places.]

 

 

2. The internal and external diameter of a hollow hemispherical shell are \(6 \ cm\) and \(10 \ cm\) respectively. If it is melted and recast into a solid cylinder of diameter \(14 \ cm\), then find the height of the cylinder.

 

Answer:

 

The height of the cylinder \(=\)  \(cm\)

 

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

 

 

3. A solid sphere of radius \(6 \ cm\) is melted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is \(5 \ cm\) and its height is \(32 \ cm\), then find the thickness of the cylinder.

Answer:

 

The thickness of the cylinder \(=\)  \(cm\)