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Here we will learn about the surface area of a hemisphere.

There are also surface area of a hemisphere worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

The **surface area of a hemisphere** is the area which covers the outer surface of a hemisphere.

To calculate this we need to know what a hemisphere is. A hemisphere is a three-dimensional object that is half of a sphere. The radius of the hemisphere is r.

To calculate the surface area of a sphere with radius r, we can use the formula

\text{Surface area of a sphere}=4\pi{r}^{2}.We can then adapt this formula, 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.

In order to calculate the total surface area we need to** add the curved surface area** **to the area of the base of the hemisphere**. The base surface is a circle and to calculate the area of the circle we need to use the formula \pi r^{2}.

Therefore the **total surface area of a hemisphere formula** is

Here are the surface area of a hemisphere formulas,

\begin{aligned} &\text{Curved surface area}=2\pi{r}^{2} \\\\ &\text{Total surface area of a hemisphere}=3\pi{r}^{2} \end{aligned}In order to calculate the surface area of a hemisphere:

**Write down the formula for the surface area of a sphere.****Find the curved surface area of the hemisphere.****If needed, find the total surface area.****Write the final answer.**

Get your free volume and surface area of a hemisphere worksheet of 20+ questions and answers. Includes reasoning and applied questions.

COMING SOONGet your free volume and surface area of a hemisphere worksheet of 20+ questions and answers. Includes reasoning and applied questions.

COMING SOON**Surface area of a hemisphere** is part of our series of lessons to support revision on **hemisphere** **shape**. You may find it helpful to start with the main hemisphere shape lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

Calculate the curved surface area of a hemisphere with radius 12 \ cm. Give your answer to 1 decimal place.

**Write down the formula for the surface area of a sphere.**

Start by considering the surface area of a sphere,

\text{Surface area}=4\pi{r}^{2}.2**Find the curved surface area of the hemisphere.**

We can adapt the surface area of a sphere to find the curved surface area of the hemisphere. We can then substitute the value of the radius.

\begin{aligned} 4\pi{r}^{2}\div 2&=2\pi{r}^{2}\\\\ &=2\pi(12)^{2}\\\\ &=904.7786…. \end{aligned}3**If needed, find the total surface area.**

The question only requires the curved surface area.

4**Write the final answer.**

The answer is 904.7786…

This rounds to give the curved surface area 904.8 \ cm^2 to 1 decimal place.

Calculate the total surface area of a hemisphere with radius 8.5 \ cm. Give your answer to 1 decimal place.

**Write down the formula for the surface area of a sphere.**

Start by considering the surface area of a sphere

\text{Surface area}=4\pi{r}^{2}.

**Find the curved surface area of the hemisphere.**

We can adapt the surface area of a sphere to find the curved surface area of the hemisphere. We can then substitute the value of the radius.

\begin{aligned} 4\pi{r}^{2}\div 2&=2\pi{r}^{2}\\\\ &=2\pi(8.5)^{2} \end{aligned}

**If needed, find the total surface area.**

We need to add the area of the the flat circle using the area of a circle, \pi r^{2}.

2\pi(8.5)^{2}+\pi(8.5)^{2}=3\pi(8.5)^{2}

**Write the final answer.**

The answer is 608.9402…

This rounds to give the curved surface area 608.9 \ cm^2 to 1 decimal place.

Calculate the total surface area of a hemisphere with diameter 6.8 \ cm. Give your answer to 1 decimal place.

**Write down the formula for the surface area of a sphere.**

Start by considering the surface area of a sphere

\text{Surface area}=4\pi{r}^{2}.

**Find the curved surface area of the hemisphere.**

We can adapt the surface area of a sphere to find the curved surface area of the hemisphere. We also need to halve the diameter, to get the radius 3.4 \ cm. We can then substitute the value of the radius

\begin{aligned} 4\pi{r}^{2}\div 2&=2\pi{r}^{2}\\\\ &=2\pi(3.4)^{2} \end{aligned}

**If needed, find the total surface area.**

We need to add the area of the the flat circle using the area of a circle, \pi r^{2}.

2\pi(3.4)^{2}+\pi(3.4)^{2}=3\pi(3.4)^{2}

**Write the final answer.**

The answer is 108.950…

This rounds to give the curved surface area 109.0 \ cm^2 to 1 decimal place.

Calculate the curved surface area of a hemisphere with radius 7 \ cm. Leave your answer in terms of \pi .

**Write down the formula for the surface area of a sphere.**

Start by considering the surface area of a sphere

\text{Surface area}=4\pi{r}^{2}.

**Find the curved surface area of the hemisphere.**

We can adapt the surface area of a sphere to find the curved surface area of the hemisphere. We can then substitute the value of the radius.

\begin{aligned} 4\pi{r}^{2}\div 2&=2\pi{r}^{2}\\\\ &=2\pi(7)^{2} \end{aligned}

**If needed, find the total surface area.**

The question only requires the curved surface area.

**Write the final answer.**

The answer is

\frac{49}{2}\pi \ \mathrm{cm}^2.

Calculate the total surface area of a hemisphere with radius 9 \ cm. Leave your answer in terms of \pi .

**Write down the formula for the surface area of a sphere.**

Start by considering the surface area of a sphere

\text{Surface area}=4\pi{r}^{2}.

**Find the curved surface area of the hemisphere.**

We can adapt the surface area of a sphere to find the curved surface area of the hemisphere.

\begin{aligned} 4\pi{r}^{2}\div 2&=2\pi{r}^{2}\\\\ &=2\pi(9)^{2} \end{aligned}

**If needed, find the total surface area.**

We need to add the area of the the flat circle using the area of a circle, \pi r^{2}.

2\pi(9)^{2}+\pi(9)^{2}=3\pi(9)^{2}

**Write the final answer.**

The answer is

243\pi \ \mathrm{cm}^2.

The total surface area of a hemisphere is 300 \ cm^{2}. Calculate the radius. Give your answer to 3 significant figures.

**Write down the formula for the surface area of a sphere.**

Start by considering the surface area of a sphere

\text{Surface area}=4\pi{r}^{2}.

**Find the curved surface area of the hemisphere.**

We can adapt the surface area of a sphere to find the curved surface area of the hemisphere. We do not have a value for the radius to substitute.

4\pi{r}^{2}\div 2=2\pi{r}^{2}

**If needed, find the total surface area.**

We need to add the area of the the flat circle using the area of a circle, \pi r^{2}.

2\pi{r}^{2}+\pi{r}^{2}=3\pi{r}^{2}

We can substitute in the value of the total surface area.

300=3\pi{r}^{2}

Then we rearrange the equation to solve it and find the radius.

\begin{aligned}
300&= 3\pi r^2\\\\
100&=\pi r^2 \\\\
\frac{100}{\pi}&=r^2\\\\
r&=\sqrt{\frac{100}{\pi}}
\end{aligned}

**Write the final answer.**

The answer is 5.6418…

This rounds to give the radius as 5.64 \ cm to 3 significant figures.

**Using the correct formula**

There are several formulas that can be used in geometry, so we need to match the correct formula to the correct context.

**Total surface area or curved surface area**

Double check whether the question requires you to find the curved surface area (csa) of the hemisphere or the total surface area (tsa) of the hemisphere.

**Rounding**

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 \pi until you round the answer at the very end of the question.

**Make sure you have the correct units**

For area we use square units such as cm^{2}.

For volume we use cube units such as cm^{3}.

**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.

1. Find the curved surface area of a hemisphere with radius 7.4 \ cm. Give your answer correct to 1 decimal place.

588.3 \ cm^2

344.1 \ cm^2

588.2 \ cm^2

392.2 \ cm^2

The curved surface area of the hemisphere can be found by using the surface area of a sphere and halving it.

\begin{aligned} \text{Curved surface area}&=4\pi r^2\div 2\\\\ &=4\pi (7.4)^2\div 2\\\\ &=344.067…\\\\ &=344.1 \mathrm{cm}^2 \ \text{(to 1 dp)} \end{aligned}

2. Find the total surface area of a hemisphere with radius 11.3 \ cm. Give your answer correct to 1 decimal place.

401.1 \ cm^2

802.3 \ cm^2

1203.4 \ cm^2

3209.2 \ cm^2

The curved surface area of the hemisphere can be found by using the surface area of a sphere and halving it. We need to add the area of the flat circle as we need the total surface area.

\begin{aligned} \text{Total surface area}&=4\pi r^2\div 2+\pi r^2\\\\ &=3\pi r^2\\\\ &=3\pi (11.3)^2\\\\ &=1203.449…\\\\ &=1203.4 \ \mathrm{cm}^2 \ \text{(to 1 dp)} \end{aligned}

3. Find the total surface area of a hemisphere with diameter 15.3 \ cm. Give your answer correct to 1 decimal place.

588.3 \ cm^2

1470.8 \ cm^2

2206.2 \ cm^2

551.6 \ cm^2

The curved surface area of the hemisphere can be found by using the surface area of a sphere and halving it. We need to add the area of the flat circle as we need the total surface area. But first we need to divide the diameter by 2 to find the radius.

r=15.3\div 2=7.65\begin{aligned} \text{Total surface area}&=4\pi r^2\div 2+\pi r^2\\\\ &=3\pi r^2\\\\ &=3\pi (7.65)^2\\\\ &=551.561…\\\\ &=551.6 \ \mathrm{cm}^2 \ \text{(to 1 dp)} \end{aligned}

4. Find the curved surface area of a hemisphere with radius 5 \ cm. Leave your answer in terms of \pi.

25\pi \ cm^2

50\pi \ cm^2

75\pi \ cm^2

100\pi \ cm^2

The curved surface area of the hemisphere can be found by using the surface area of a sphere and halving it.

\begin{aligned} \text{Curved surface area}&=4\pi r^2\div 2\\\\ &=4\pi (5)^2\div 2\\\\ &=50\pi\\\\ &=50\pi \ \mathrm{cm}^2 \end{aligned}

5. Find the total surface area of a hemisphere with radius 11 \ cm. Leave your answer in terms of \pi.

363\pi \ cm^2

121\pi \ cm^2

242\pi \ cm^2

484\pi \ cm^2

The curved surface area of the hemisphere can be found by using the surface area of a sphere and halving it. We need to add the area of the flat circle as we need the total surface area.

\begin{aligned} \text{Total surface area}&=4\pi r^2\div 2+\pi r^2\\\\ &=3\pi r^2\\\\ &=3\pi (11)^2\\\\ &=363\pi\\\\ &=363\pi \ cm^2 \end{aligned}

6. The total surface area of a hemisphere is 7500 \ cm^{2}. Find the radius of the hemisphere. Give your answer to 3 significant figures.

48.9 \ cm

28.2 \ cm

69.1 \ cm

24.4 \ cm

The total surface area of the hemisphere can be found by using the surface area of a sphere and halving it then adding the area of the flat circle.

This gives 3\pi r^{2}. We can form an equation using the given value and rearrange to solve it.

\begin{aligned} \text{Total surface area}&=4\pi r^2\div 2+\pi r^2\\\\ \text{Total surface area}&=3\pi r^2\\\\ 7500&=3\pi r^2\\\\ 2500&=\pi r^2\\\\ \frac{2500}{\pi}&=r^2\\\\ r&=\sqrt{\frac{2500}{\pi}}\\\\ r&=28.2094…\\\\ r&=28.2 \ cm \ \text{(to 3 sf)} \end{aligned}

1. A hemisphere has a radius of 13 \ cm.

Calculate the total surface area of the hemisphere.

Give your answer in terms of \pi .

**(3 marks)**

Show answer

CSA: 338\pi, circular base: 169\pi OR 3\pi r^{2}

**(1)**

Evidence of adding CSA and circular base.

**(1)**

**(1)**

2. An artist is making a sculpture of a hemisphere with diameter 8 metres.

He needs to coat the total surface area in paint.

A tin of paint covers an area of 20m^{2}.

Calculate how many tins of paint the artist will need to buy.

**(4 marks)**

Show answer

Radius = 4

**(1)**

**(1)**

**(1)**

7.539… = 8 tins of paint

**(1)**

3. A hemisphere has a total surface area of 800 \ cm^{2}.

Calculate its diameter.

Give your answer correct to 3 significant figures.

**(4 marks)**

Show answer

800=3\pi{r}^{2}

**(1)**

**(1)**

**(1)**

**(1)**

You have now learned how to:

- Find the curved surface area of a hemisphere
- Find the total surface area of a hemisphere
- Solve problems involving the surface area of a hemisphere

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