Theory:

1. The diameter of an orange is \(8 \ cm\). Calculate the total surface area of the half orange.
 
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Solution:
 
Diameter of an orange, \(d\) \(=\) \(8 \ cm\)
 
Radius of an orange, \(r\) \(=\) d2=82=4cm
 
A half orange is in the shape of a hemisphere.
 
Total surface area of a hemisphere \(=\) \(3 \pi r^2\) sq. units
 
\(=\) 3×227×42
 
\(=\) 3×227×16
 
\(=\) \(150.86\)
  
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
 
\(=\) 2×227×52+32
 
\(=\) 2×227×25+9
 
\(=\) 2×227×34
 
\(=\) \(213.7\)
 
The curved surface area of the hemispherical shell is \(213.7\) \(cm^2\).
 
Important!
The value of \(\pi\) should be taken as \(\frac{22}{7}\) unless its value is shared in the problem.