Formula sheet
Surface area of sphere
4πr² is given on the exam formula sheet. You must still use the radius (not diameter), square it, and know this is the surface area of a full sphere, a hemisphere's curved part is only half of it.
What the symbols mean
- r Radius of the sphere (length unit). Halve the diameter if only d is given.
- π Pi ≈ 3.142 or 22/7.
Given in the exam, or memorise?
4πr² is given on the exam formula sheet. You must still use the radius (not diameter), square it, and know this is the surface area of a full sphere, a hemisphere's curved part is only half of it.
Why it works
The sphere's surface equals four of its great-circle areas.
- A great circle through the centre has area πr².
- Careful measurement shows the whole curved surface equals exactly four such circles.
- So surface area = 4 × πr² = 4πr².
Worked example 1
Find the surface area of a sphere of radius 7 cm. (Use π = 22/7)
- Surface area = 4πr²
- = 4 × 22/7 × 7²
- = 4 × 22/7 × 49
- = 4 × 154 = 616
Worked example 2
A sphere has surface area 1386 cm². Find its radius.
(Use π = 22/7)
- Surface area = 4πr²
- 1386 = 4 × 22/7 × r² = (88/7) r²
- r² = 1386 × 7 ÷ 88 = 110.25
- r = √110.25 = 10.5
Where students go wrong
- Using 2πr² (a hemisphere's curved surface) instead of 4πr² for a full sphere.
- Putting the diameter into r, halve it first.
- Forgetting to square r.
- Answering in cm instead of cm².
Use it with
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
How do I find the surface area of a hemisphere?
A solid hemisphere has a curved part equal to half a sphere, 2πr², plus a flat circular face πr², giving 3πr² in total. If only the curved dome is wanted, use 2πr² alone.
So do not just halve 4πr² blindly, decide whether the flat circle is included.
The question gives the diameter of a ball. What now?
Halve the diameter to get the radius, because 4πr² needs r. A ball of diameter 14 cm has r = 7 cm, so the surface area is 4π × 7² = 616 (with π = 22/7).
Dropping the diameter straight in would make the answer four times too large.
Is 4πr² the surface area or the volume?
It is the surface area, in cm², because r is squared. The volume of a sphere is (4/3)πr³, in cm³, where r is cubed.
A quick check is the power of r and the unit: squared with cm² means surface area, cubed with cm³ means volume. Do not swap the two.