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Lesson 13 of 16
Lesson 13 of 16
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Surface area of cylinders
I can find the surface area of cylinders.
Lesson details
Key learning points
- Drawing the net of a cylinder helps deduce the formula for the surface area.
- The formula can be used to find the surface area of any cylinder.
- Unknown lengths can be found when the surface area is known.
Keywords
Cylinder - a 3D shape with a base that is a circle and a parallel opposite face that is identical. Cross sections parallel to the base are uniform.
Common misconception
Pupils may overlook whether they have been given the diameter or radius of the circles.
Encourage pupils to always write down the radius before any calculation of the surface area is started.
Use examples where the cylinder is orientated in various ways to highlight that the words height/length/depth can be used interchangeably depending on the context.
Teacher tip
Licence
This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
Lesson video
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Prior knowledge starter quiz
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6 Questions
Q1.The area of a rectangle with a width of 6 cm and a length of 14 cm is $$\text{ cm}^2$$.
The area of a rectangle with a width of 6 cm and a length of 14 cm is $$\text{ cm}^2$$.
Correct Answer: 84, eighty four
84, eighty four
Q2.What is the area of a circle, with a radius of 5 cm?
What is the area of a circle, with a radius of 5 cm?
$$5\pi\text{ cm}$$
$$25\pi\text{ cm}$$
$$5\pi\text{ cm}^2$$
$$10\pi\text{ cm}^2$$
Correct answer: $$25\pi\text{ cm}^2$$
$$25\pi\text{ cm}^2$$
Q3.The area of a circle with a diameter of 16 cm, has an area of $$\pi \text{ cm}^2$$.
The area of a circle with a diameter of 16 cm, has an area of $$\pi \text{ cm}^2$$.
Correct Answer: 64, sixty four
64, sixty four
Q4.The surface area is the total area of all the surfaces of a closed shape. The surfaces include all faces and any curved surfaces.
The surface area is the total area of all the surfaces of a closed shape. The surfaces include all faces and any curved surfaces.
Correct Answer: 3D, three-dimensional, 3d, 3-D, 3-d
3D, three-dimensional, 3d, 3-D, 3-d
Q5.A cuboid has dimensions 4 cm, 6 cm and 15 cm. Select all the areas of its surfaces.
A cuboid has dimensions 4 cm, 6 cm and 15 cm. Select all the areas of its surfaces.
$$10\text{ cm}^2$$
Correct answer: $$24\text{ cm}^2$$
$$24\text{ cm}^2$$
Correct answer: $$60\text{ cm}^2$$
$$60\text{ cm}^2$$
Correct answer: $$90\text{ cm}^2$$
$$90\text{ cm}^2$$
$$360\text{ cm}^2$$
Q6.A cube has a surface area of 294 $$\text{ cm}^2$$. The area of each face is $$\text{ cm}^2$$.
A cube has a surface area of 294 $$\text{ cm}^2$$. The area of each face is $$\text{ cm}^2$$.
Correct Answer: 49
49
Assessment exit quiz
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6 Questions
Q1.A cylinder is a type of prism. True or false?
A cylinder is a type of prism. True or false?
True - it has a uniform cross-section throughout the length.
Correct answer: False - the uniform cross-section is not a polygon.
False - the uniform cross-section is not a polygon.
Q2.A is a 3D shape with a base that is a circle and a parallel opposite face that is identical. A cross-section of a cylinder made parallel to the base is congruent to the base.
A is a 3D shape with a base that is a circle and a parallel opposite face that is identical. A cross-section of a cylinder made parallel to the base is congruent to the base.
Correct Answer: cylinder
cylinder
Q3.Which of these is a net of a cylinder?
Which of these is a net of a cylinder?
Correct Answer: An image in a quiz
Q4.Which of these is the formula for the surface area of any cylinder, where $$r$$ is the radius and $$h$$ is the height?
Which of these is the formula for the surface area of any cylinder, where $$r$$ is the radius and $$h$$ is the height?
$$\text{Surface area}=\pi r^2+\pi rh$$
$$\text{Surface area}=2\pi r^2+\pi rh$$
Correct answer: $$\text{Surface area}=2\pi r^2+2\pi rh$$
$$\text{Surface area}=2\pi r^2+2\pi rh$$
Correct answer: $$\text{Surface area}=2\pi r(r+h)$$
$$\text{Surface area}=2\pi r(r+h)$$
$$\text{Surface area}=2(\pi r)^2 +2 \pi rh $$
Q5.The surface area of a cylinder with a diameter of 10 cm and a height of 7 cm is $$\pi \text{ cm}^2.$$
The surface area of a cylinder with a diameter of 10 cm and a height of 7 cm is $$\pi \text{ cm}^2.$$
Correct Answer: 120
120
Q6.A cylinder has a surface area of $$72\pi \text{ cm}^2$$ and a radius of 3 cm. What is the length of the cylinder?
A cylinder has a surface area of $$72\pi \text{ cm}^2$$ and a radius of 3 cm. What is the length of the cylinder?
8 cm
Correct answer: 9 cm
9 cm
10 cm
10.5 cm