Sheet № 214 · Higher only · AQA · Edexcel · OCR
Volume of a Hemisphere –
Volume of a hemisphere is a Higher-tier GCSE Maths topic tested on AQA, Edexcel, and OCR papers. A hemisphere is exactly half of a sphere, so you halve the sphere volume formula. Questions may also ask for the total surface area, which includes the curved surface and the flat circular base. This guide explains both formulas, works through
§Key definitions
Question:
Find the volume of a hemisphere with radius 6 cm. Give your answer in terms of π.
Answer:
The volume is 144π cm³.
Q1 (Higher):
Find the volume of a hemisphere with radius 10 cm. Give your answer to 1 decimal place.
Q2 (Higher):
Find the total surface area of a hemisphere with radius 7 cm. Give your answer in terms of π.
Q3 (Higher):
A hemisphere has a total surface area of 75π cm². Find the radius.
§Formulas to memorise
Volume of a sphere = (4/3)πr³
Volume of a hemisphere = (2/3)πr³
Curved surface area of a hemisphere = 2πr²
Total surface area of a hemisphere = 2πr² + πr² = 3πr²
Substitute into V = (2/3)πr³.
Add them together: total SA = 3πr².
Worked example
Find the volume of a hemisphere with radius 6 cm. Give your answer in terms of π.
This topic is Higher only, but this example uses straightforward numbers.
⚠ Common mistakes
- ✗Using the full sphere formula instead of halving. Always divide the sphere volume by 2: V = (2/3)πr³, not (4/3)πr³.
- ✗Forgetting the flat base in surface area. The total surface area of a hemisphere is 3πr², not just the curved part (2πr²). Read the question carefully to see if it asks for curved SA or total SA.
- ✗Using diameter instead of radius. If given the diameter, halve it before substituting into the formula.
✦ Exam tips
- →Formulas for sphere volume and surface area are given on the formula sheet — but you must remember to halve them for a hemisphere.
- →Leave your answer in terms of π if the question says "give your answer in terms of π" — do not convert to a decimal.
- →Composite shape questions (hemisphere + cone, hemisphere + cylinder) are common — calculate each part separately and add.
- →When working backwards to find r, remember to take the cube root at the end.