5. Example problems of a hemisphere and hollow hemisphere

1. The diameter of an orange is \(8 \ cm\). Calculate the total surface area of the half orange.

 

 

Solution:

 

Diameter of an orange, \(d\) \(=\) \(8 \ cm\)

 

Radius of an orange, \(r\) \(=\) $\frac{d}{2}=\frac{8}{2}=4\mathit{cm}$

 

A half orange is in the shape of a hemisphere.

 

Total surface area of a hemisphere \(=\) \(3 \pi r^2\) sq. units

 

\(=\) $3\times \frac{22}{7}\times 4^2$

 

\(=\) $3\times \frac{22}{7}\times 16$

 

\(=\) \(150.86\)

  

The total surface area of the half orange is \(150.86 \ cm^2\).

 

 

2. If the inner and outer radius of the hemispherical shell is \(3 \ cm\) and \(5 \ cm\), find the thickness and the curved surface area of the shell.

 

Solution:

 

Inner radius, \(r\) \(=\) \(3 \ cm\)

 

Outer radius, \(R\) \(=\) \(5 \ cm\)

 

Thickness \(=\) \(R - r\)

 

\(=\) \(5 - 3 = 2\)

 

The thickness of the shell is \(2 \ cm\).

 

Curved surface area \(=\) \(2 \pi (R^2 + r^2)\) sq. units