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Sphere
Here we will learn about spheres, including how to find the volume and surface area of a sphere.
There are also sphere worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if youβre still stuck.
What is a sphere shape?
A sphere shape is a three dimensional shape where every point of its surface is equidistant (the same distance) from the centre of the sphere. The distance from the centre of a sphere to its surface is called the radius. A sphere has no vertices.
A hemisphere is half a sphere.
What is a sphere shape?
Volume of a sphere shape
The volume of a sphere is the amount of space there is inside a sphere.
The formula for the volume of a sphere is:
katex is not definedE.g. Find the volume of the sphere
This sphere has a radius of katex is not defined.
katex is not definedStep-by-step guide: Volume of a sphere
Surface area of a sphere shape
The surface area of a sphere is the area which covers the outer surface of a sphere.
The formula for the surface area of a sphere is:
katex is not definedE.g. Find the surface area of the sphere
This sphere has a radius of katex is not defined.
katex is not definedStep-by-step guide: Surface area of a sphere
How to calculate the volume or surface area of a sphere
In order to calculate the volume of a sphere or the surface area of a sphere:
- Write down the formula.
- Substitute the given values.
- Work out the calculation
- Write the final answer.
How to calculate the volume or surface area of a sphere
Volume and surface area of a sphere worksheet
Get your free sphere shape worksheet of 20+ volume and surface area of a sphere questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREE Volume and surface area of a sphere worksheet
Get your free sphere shape worksheet of 20+ volume and surface area of a sphere questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREESphere shape examples
Example 1: volume of a sphere
Calculate the volume of a sphere of radius katex is not defined Give your answer to katex is not defined significant figures.
- Write down the formula for the volume of a sphere.
2Substitute the given values into the formula.
katex is not defined3Complete the calculation.
katex is not defined4Write the final answer, including the units.
The radius is given in centimetres so the volume will be cubic centimetres.
The volume of the sphere is katex is not defined.
Example 2: volume of a sphere, given the diameter
Calculate the volume of a sphere with a diameter of katex is not defined. Write your answer in terms of katex is not defined.
Write down the formula for the volume of a sphere.
Substitute the given values into the formula.
The diameter is twice the length of the radius. To calculate the radius, we need to first divide the diameter by katex is not defined
katex is not defined
The radius is katex is not defined Substituting this into the formula for the volume of a sphere, we have
katex is not defined
Complete the calculation.
Write the final answer, including the units.
The radius is given in centimetres so the volume will be cubic centimetres.
The volume of the sphere is katex is not defined.
Example 3: volume of a hemisphere
Calculate the volume of a hemisphere of radius katex is not defined. Write your answer to katex is not defined decimal places.
Write down the formula for the volume of a sphere.
Substitute the given values into the formula.
Complete the calculation.
But this is for a whole sphere. We need a hemisphere, so we need to divide by katex is not defined
katex is not defined
Write the final answer, including the units.
The radius is given in centimetres so the volume will be cubic centimetres.
The volume of the hemisphere is katex is not defined
Example 4: surface area of a sphere
Calculate the surface area of a sphere with radius katex is not defined. Write your answer to katex is not defined decimal place.
Write down the formula for the surface area of a sphere.
Substitute the given values into the formula.
Here we know the radius of the sphere is katex is not defined so we substitute katex is not defined into the formula for the surface area.
katex is not defined
Complete the calculation.
Write the final answer, including the units.
The radius is measured in centimetres so the surface area is measured in square centimetres katex is not defined, with the solution rounded to katex is not defined decimal place.
The surface area of the sphere is katex is not defined.
Example 5: surface area of a sphere given the diameter β in terms of Ο
Find the surface area of a sphere with the diameter of katex is not defined Leave your answer in terms of katex is not defined.
Write down the formula for the surface area of a sphere.
Substitute the given values into the formula.
The diameter of the sphere is katex is not defined and so we need to use this to calculate the radius and hence the surface area of the sphere.
katex is not defined
The radius of the sphere is katex is not defined
We now know the radius of the sphere is katex is not defined so we substitute katex is not defined into the formula for the surface area.
katex is not defined
Complete the calculation.
Write the final answer, including the units.
The radius is measured in centimetres so the surface area is measured in square centimetres katex is not defined, with the solution in terms of katex is not defined.
The surface area of the sphere is katex is not defined.
Example 6: total surface area of a hemisphere
Find the total surface area of a hemisphere with a radius katex is not defined Write your answer to katex is not defined significant figures.
Write down the formula for the surface area of a sphere.
For the surface area of a hemisphere we need half of the surface area of a sphere and add it on to the area of the flat circular base. The formula can be adapted.
katex is not defined
Substitute the given values into the formula.
Complete the calculation.
Write the final answer, including the units.
The radius is measured in centimetres so the surface area is measured in square centimetres katex is not defined, with the solution rounded to katex is not defined significant figures.
The surface area of the sphere is katex is not defined.
Common misconceptions
- Using the correct formula
There are several formulas that can be used, so we need to match the correct formula to the correct context.
- Rounding
It is important to not round the answer until the end of the calculation. This will mean your final answer is accurate.
- Make sure you have the correct units
For area we use square units such as katex is not defined
For volume we use cube units such as katex is not defined
- Using the radius or the diameter
It is a common error to mix up radius and diameter. Remember the radius is half of the diameter.
Practice sphere shape questions
1. Find the volume of a sphere with radius katex is not defined Write your answer to katex is not defined decimal places.
We are finding the volume of a sphere so we substitute the value of the radius katex is not defined into the formula katex is not defined
katex is not defined
2. Find the volume of a sphere with radius katex is not defined Leave your answer in terms of katex is not defined.
We are finding the volume of a sphere so we substitute the value of the radius into the formula katex is not defined. As the diameter is twice the length of the radius, katex is not defined
katex is not defined
3. Find the volume of a hemisphere with radius katex is not defined Write your answer to katex is not defined decimal place.
We are finding the volume of a hemisphere, so we need to calculate half of the volume of a sphere using the radius katex is not defined and the formula: katex is not defined
katex is not defined
4. Find the surface area of a sphere with radius katex is not defined Give your answer to katex is not defined decimal places.
We are finding the surface area of a sphere, so we substitute the value of the radius katex is not defined into the formula katex is not defined
katex is not defined
5. Find the surface area of a sphere with a diameter of katex is not defined Leave your answer in terms of katex is not defined
We are finding the surface area of a sphere, so we need to calculate the value of the radius using the diameter, then substitute the value of the radius into the formula for the surface area.
katex is not defined
The radius katex is not defined
katex is not defined
6. Find the surface of a hemisphere with radius katex is not defined Give your answer to katex is not defined decimal place.
We need to find the curved surface area by finding half of the surface area of a sphere. Then we add on the area of the circular top.
katex is not defined
Sphere shape GCSE questions
1. Here is a sphere with a radius katex is not defined
Calculate the volume of the sphere.
Write your answer to katex is not defined decimal place.
(2 marks)
(1)
katex is not defined
(1)
2. A tennis ball has a radius of katex is not defined Each tennis ball is covered in felt. Calculate the area of the felt required to cover the ball to the nearest square millimetre.
(4 marks)
(1)
katex is not defined
(1)
katex is not defined
(1)
katex is not defined
(1)
3. A container is a hemisphere with a diameter of katex is not defined
Sand fills the container at a rate of katex is not defined per minute.
How long does it take to fill the container?
Give your answer to the nearest minute.
(3 marks)
(1)
katex is not defined
(1)
katex is not defined minutes
(1)
4. A sphere has a surface area of katex is not defined
Calculate its volume.
Give your answer to katex is not defined significant figures.
(3 marks)
(1)
katex is not defined
(1)
katex is not defined
(1)
Learning checklist
You have now learned how to:
- Find the volume of a sphere
- Find the surface area of a sphere
- How to solve problems involving spheres
The next lessons are
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