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Multiplying fractions Substitution Area of a circle Rounding numbers Volume of a sphere Surface area of a sphereThis topic is relevant for:
Here we will learn about the hemisphere shape, including what a hemisphere is and how to calculate the volume of a hemisphere and the surface area of a hemisphere.
There are also hemisphere shape worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if youβre still stuck.
A hemisphere shape is a three-dimensional shape that is half of a sphere.
To visualise this letβs look at a sphere. A sphere is a 3D shape where every point of its surface is equidistant (the same distance) from the centre of the sphere.
It has a radius
A hemisphere is half of a sphere. The prefix βhemiβ means half.
You may have come across the word hemisphere in the real life context of planet Earth. We can split the world into equal halves β the northern hemisphere and the southern hemisphere.
A hemisphere is a geometric shape which has a curved surface area and a flat face, which is a circle.
A hemisphere has no vertices and one edge. It is not made up of polygons, so it is not a polyhedron.
Faces:
Edges:
Vertices:
The volume of a hemisphere is based on the volume of a sphere.
To calculate the volume of a sphere, where r is the radius of the sphere, we use the formula
To find the volume of a hemisphere we halve the volume of a sphere.
Here is the volume of a hemisphere formula, for a hemisphere with radius
or
Step-by-step guide: Volume of a hemisphere
The surface area of a hemisphere is based on the surface area of a sphere.
To calculate the surface area of a sphere with radius r, we can use the formula
So to find the curved surface area of the hemisphere we need to halve the surface area of the sphere.
However this would only give the curved surface area. If we want the total surface area, we need to add the area of the base.
The area of the base, which is a circle, is given by
Here is the surface area of a hemisphere formula, for a hemisphere with radius
.
Step-by-step guide: Surface area of a hemisphere
In order to work out the volume or surface area of a hemisphere:
Get your free hemisphere shape worksheet of 20+ questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREEGet your free hemisphere shape worksheet of 20+ questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREEFind the volume of a hemisphere with radius Give your answer correct to significant figures.
We need to consider the formula for the volume of a sphere.
2Adapt the formula for the question.
The formula needs to be halved for the volume of a hemisphere.
3Substitute in the value.
Then we substitute in the value in place of
4Write the final answer.
The answer is
This rounds to give (to significant figures) as the volume of the hemisphere.
Find the volume of a hemisphere with radius Leave your answer in terms of
Write down the formula for the sphere.
We need to consider the formula for the volume of a sphere.
Adapt the formula for the question.
The formula needs to be halved for the volume of a hemisphere.
Substitute in the value.
Then we substitute in the value in place of
Write the final answer.
The volume of the hemisphere is .
Find the curved surface area of a hemisphere with diameter Give your answer correct to decimal place.
Write down the formula for the sphere.
We need to consider the formula for the surface area of a sphere.
Adapt the formula for the question.
The formula needs to be halved for the curved surface area of a hemisphere.
Substitute in the value.
We have been given a diameter We need to divide the diameter by to get the radius. So we substitute in the value in place of
Write the final answer.
The answer is
This rounds to give (to decimal place) as the curved surface area of the hemisphere.
Find the total surface area of a hemisphere with radius Give your answer correct to significant figures.
Write down the formula for the sphere.
We need to consider the formula for the surface area of a sphere.
Adapt the formula for the question.
The formula needs to be halved for the curved surface area of a hemisphere.
But, we need to also add the area of the circular base to get the total surface area of the hemisphere.
Substitute in the value.
Then we substitute in the value in place of
Write the final answer.
The answer is
This rounds to give (to significant figures) as the total surface area of the hemisphere.
Find the curved surface area of a hemisphere with radius Leave your answer in terms of
Write down the formula for the sphere.
We need to consider the formula for the surface area of a sphere.
Adapt the formula for the question.
The formula needs to be halved for the curved surface area of a hemisphere.
Substitute in the value.
Then we substitute in the value in place of
Write the final answer.
The curved surface area of the hemisphere is .
Find the total surface area of a hemisphere with diameter Leave your answer in terms of
Write down the formula for the sphere.
We need to consider the formula for the surface area of a sphere.
Adapt the formula for the question.
The formula needs to be halved for the curved surface area of a hemisphere.
But, we need to also add the area of the circular base to get the total surface area of the hemisphere.
Substitute in the value.
We have been given a diameter We need to divide the diameter by to get the radius. So we substitute in the value in place of
Write the final answer.
The total surface area of the hemisphere is .
There are several formulas that can be used in geometry, so we need to match the correct formula to the correct context.
Double check whether the question requires you to find the curved surface area of a hemisphere or the total surface area of a hemisphere.
It is important to not round the answer until the end of the calculation. This will mean your final answer is accurate. It is useful to keep your answer in terms of until you round the answer at the very end of the question.
For area we use square units such as
For volume we use cube units such as
It is a common error to mix up radius and diameter. Remember the radius is half of the diameter.
1. Find the volume of a hemisphere with radius Give your answer correct to significant figures.
We need to halve the formula for the volume of a sphere, and then substitute the value of in place of
2. Find the volume of a hemisphere with diameter Leave your answer in terms of
We have been given the diameter which we need to divide by to get the radius. We need to halve the formula for the volume of a sphere, and then substitute the value of in place of
3. Find the curved surface area of a hemisphere with radius Give your answer correct to significant figures.
We need to halve the formula for the surface area of a sphere to find the curved surface area of a hemisphere
Then we substitute the value of in place of
4. Find the curved surface area of a hemisphere with radius Leave your answer in terms of .
We need to halve the formula for the surface area of a sphere to find the curved surface area of a hemisphere
Then we substitute the value of in place of
5. Find the total surface area of a hemisphere with radius Give your answer correct to significant figures.
We need to halve the formula for the surface area of a sphere and add on the circular base to find the total surface area of a hemisphere
Then we substitute the value of in place of
6. Find the total surface area of a hemisphere with radius Leave your answer in terms of .
We need to halve the formula for the surface area of a sphere and add on the circular base to find the total surface area of a hemisphere
Then we substitute the value of in place of
1. Calculate the total surface area of a hemisphere with radius
(3 marks)
CSA: Circular base: or
(1)
Evidence of adding CSA and circular area.
(1)
(1)
2. Mary has a large hemisphere container in her garden.
It has a diameter of metres.
She wants to fill the container with sand.
Sand comes in bags of and the cost of a bag of sand is
Calculate the total cost of the sand to fill the container.
(5 marks)
Radius is .
(1)
(1)
(1)
(1)
(1)
3. A hemisphere has a total surface area of
Calculate its diameter.
Give your answer correct to significant figures.
(4 marks)
(1)
(1)
(1)
(1)
You have now learned how to:
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