The formula for calculating the volume of a hemisphere is:
Volume (V) = (2/3)πr³
Where:
- V = volume of the hemisphere
- r = radius of the hemisphere (distance from centre to surface)
- π (pi) ≈ 3.1416, a constant used in circular and spherical calculations
Volume of a hemisphere Quick Overview
| Formula | Variables & Meaning | When it is used |
|---|---|---|
| V = (2/3)πr³ | r = radius, π = 3.1416 | Used to find how much space a hemisphere occupies inside (its capacity or internal volume) |
What is Volume of a hemisphere in maths?
In mathematics, a hemisphere is half of a sphere. Its volume represents half of the space occupied by a full sphere. The formula helps calculate the capacity of half-spherical objects such as bowls, domes, tanks, and bubbles.
A sphere’s volume is given by V = (4/3)πr³.
Since a hemisphere is half of a sphere, its volume is:
V = (1/2) × (4/3)πr³
⟹ V = (2/3)πr³
This formula helps measure how much liquid or material can fill a half-spherical object.
In real life, it is applied in designing water tanks, domes, sports equipment, and 3D modelling.
In exams like CUET, SSC, and JEE, questions often involve substituting the radius into the formula and calculating the result.
Solved Example
Example 1 : Find the volume of a hemisphere with radius 7 cm.
Solution :
Step 1: V = (2/3)πr³
Step 2: = (2/3) × 3.1416 × 7³
Step 3: = (2/3) × 3.1416 × 343
Step 4: = (2/3) × 1078.0 = 718.6 cm³
So, the volume of a hemisphere is 718.6 cm³
Example 2 : Find the volume of a hemisphere with radius 10 m.
Solution :
Step 1: Volume = (2/3)πr³
Step 2: = (2/3) × 3.1416 × 10³
Step 3: = (2/3) × 3.1416 × 1000
Step 4: = (2/3) × 3141.6 = 2094.4 m³
So, the volume of a hemisphere is 2094.4 m³
FAQs on volume of a hemisphere
Q1. What is the difference between the volume of a sphere and a hemisphere?
A hemisphere’s volume is half of a sphere’s volume.
Q2. Why do we multiply by 2/3 in the formula?
Because it is derived from half of the sphere’s formula (4/3πr³ ÷ 2 = 2/3πr³).
Q3. What unit is used for volume?
Volume is measured in cubic units such as cm³, m³, or litres.
Q4. Can this formula be used for hollow hemispheres?
No, this formula is for solid hemispheres. Hollow ones need inner and outer radii.
Q5. Where is this formula used in real life?
Used in calculating capacity of bowls, domes, and containers shaped like half-spheres.
Q6. Is this topic important for exams?
Yes, it’s frequently asked in SSC, CUET, NEET, and JEE geometry sections.