Hemisphere Calculator

How the Hemisphere Calculator Works:

The calculator offers five calculation options based on the given parameter. You can select the appropriate option, provide the necessary input, and the calculator will generate all relevant properties.

1. Calculate Circumference (C), Volume (V), Curved Surface Area (A), Base Surface Area (B), Total Surface Area (K) | Given Radius (r)

   • Input: Radius $r$
   • Formulas:
     • Base Circumference $C = 2 \pi r$
     • Volume $V = \frac{2}{3} \pi r^3$
     • Curved Surface Area $A = 2 \pi r^2$
     • Base Surface Area $B = \pi r^2$
     • Total Surface Area $K = A + B = 3 \pi r^2$
   • Example: If $r = 5$, then:
     • $C = 2 \cdot 3.14159 \cdot 5 = 31.4159$
       
     • $V = \frac{2}{3} \cdot 3.14159 \cdot 5^3 = 261.799$
       
     • $A = 2 \cdot 3.14159 \cdot 5^2 = 157.08$
       
     • $B = 3.14159 \cdot 5^2 = 78.5398$
       
     • $K = 3 \cdot 3.14159 \cdot 5^2 = 235.619$
       

2. Calculate Radius (r), Circumference (C), Curved Surface Area (A), Base Surface Area (B), Total Surface Area (K) | Given Volume (V)

   • Input: Volume $V$
   • Formulas:
     • Radius $r = \left( \frac{3V}{2 \pi} \right)^{\frac{1}{3}}$
     • Use the calculated $r$ to find other properties as in option 1.
   • Example: If $V = 100$, then:
     • $r = \left( \frac{3 \cdot 100}{2 \cdot 3.14159} \right)^{\frac{1}{3}} = 3.633$
       
     • Use $r = 3.633$ to calculate $C, A, B, K$.

3. Calculate Radius (r), Circumference (C), Volume (V), Base Surface Area (B), Total Surface Area (K) | Given Curved Surface Area (A)

   • Input: Curved Surface Area $A$
   • Formulas:
     • Radius $r = \sqrt{\frac{A}{2 \pi}}$
     • Use the calculated $r$ to find other properties as in option 1.
   • Example: If $A = 50$, then:
     • $r = \sqrt{\frac{50}{2 \cdot 3.14159}} = 2.821$
       
     • Use $r = 2.821$ to calculate $C, V, B, K$.

4. Calculate Radius (r), Circumference (C), Volume (V), Curved Surface Area (A), Base Surface Area (B) | Given Total Surface Area (K)

   • Input: Total Surface Area $K$
   • Formulas:
     • Radius $r = \sqrt{\frac{K}{3 \pi}}$
     • Use the calculated $r$ to find other properties as in option 1.
   • Example: If $K = 100$, then:
     • $r = \sqrt{\frac{100}{3 \cdot 3.14159}} = 3.257$
       
     • Use $r = 3.257$ to calculate $C, V, A, B$.

5. Calculate Radius (r), Volume (V), Curved Surface Area (A), Base Surface Area (B), Total Surface Area (K) | Given Base Circumference (C)

   • Input: Base Circumference $C$
   • Formulas:
     • Radius $r = \frac{C}{2 \pi}$
     • Use the calculated $r$ to find other properties as in option 1.
   • Example: If $C = 20$, then:
     • $r = \frac{20}{2 \cdot 3.14159} = 3.183$
       
     • Use $r = 3.183$ to calculate $V, A, B, K$.