Circumference and circle
A bicycle wheel, a basketball hoop, a pizza... they are all circumferences or circles. They look the same, but they are not, and mixing them up is the most typical mistake in this topic.
Circumference and circle
Identify the names of the following coloured regions inside or around the circle: A: Region bounded by two radii. B: Region bounded by two concentric circles (like a…
Identify the names of the following coloured regions inside or around the circle:
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A: Region bounded by two radii.
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B: Region bounded by two concentric circles (like a doughnut).
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C: Half of a circle.
Elements of the circumference
If the diameter is drawn in full, it divides the circle into two equal semicircles.
In the following drawing of a circle with centre $O$, identify the elements labelled with letters. State which corresponds to the radius, which to the diameter, and…
In the following drawing of a circle with centre $O$, identify the elements labelled with letters. State which corresponds to the radius, which to the diameter, and which to the chord.
If a $2$ euro coin has a radius of $12,875$ mm, what is its diameter? Express the answer in millimetres.
If a $2$ euro coin has a radius of $12,875$ mm, what is its diameter? Express the answer in millimetres.
Positions of a point and a line relative to the circumference
A point can be inside (at a smaller distance from the centre than the radius), be on the circumference (at the same distance, the radius), or be outside (at a greater distance).
Look at the position of the lines $r$, $s$ and $t$ relative to the circle with centre $C$. Classify each line as tangent, secant or exterior.
Look at the position of the lines $r$, $s$ and $t$ relative to the circle with centre $C$. Classify each line as tangent, secant or exterior.
Given a circle with centre at point $C$ and a radius of $5$ cm, state whether the following points are inside, outside or on the circle: Point $P$: is $3$ cm from $C$.…
Given a circle with centre at point $C$ and a radius of $5$ cm, state whether the following points are inside, outside or on the circle:
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Point $P$: is $3$ cm from $C$.
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Point $Q$: is $5$ cm from $C$.
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Point $R$: is $7$ cm from $C$.
Length of the circumference
If you wrap a piece of string around a circumference and then unwrap it, its length is always a little more than $3$ times the diameter, however much the size of the circle changes. That number is $\pi$ (pi), $\pi \approx 3{,}14$.
Álex wants to put a strip of LED lights around the edge of his circular mirror. If the radius of the mirror is $40$ cm, what is the minimum length in centimetres of LED…
Álex wants to put a strip of LED lights around the edge of his circular mirror. If the radius of the mirror is $40$ cm, what is the minimum length in centimetres of LED strip he will need to buy? (Use $\pi \approx 3,14$).
The wheel of a mountain bike has a total radius of $35\text{ cm}$. If the cyclist travels a distance of $1,1\text{ kilometres}$ in a straight line: a) How many metres…
The wheel of a mountain bike has a total radius of $35\text{ cm}$. If the cyclist travels a distance of $1,1\text{ kilometres}$ in a straight line:
- a) How many metres does the bicycle travel in a single revolution of the wheel?
- b) How many complete revolutions will the wheel have made by the end of the ride?
(Given: $1\text{ km} = 1000\text{ m}$; use $\pi \approx 3,14$).
Area of the circle
A basketball player is practising free throws. The circle painted in the key has a diameter of $3,6$ metres. What is the length of the radius of this circle?
A basketball player is practising free throws. The circle painted in the key has a diameter of $3,6$ metres. What is the length of the radius of this circle?
A pizzeria offers an individual pizza with a diameter of $20$ cm. Calculate the area of the pizza to find out how much space it will take up in the box. (Use…
A pizzeria offers an individual pizza with a diameter of $20$ cm. Calculate the area of the pizza to find out how much space it will take up in the box. (Use $\pi \approx 3,14$).
A pizzeria has two offers for its artisan pizzas: Offer A: One family pizza with a diameter of $40\text{ cm}$. Offer B: Two medium pizzas with a diameter of…
A pizzeria has two offers for its artisan pizzas:
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Offer A: One family pizza with a diameter of $40\text{ cm}$.
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Offer B: Two medium pizzas with a diameter of $20\text{ cm}$ each.
If both offers cost the same, calculate the surface area of pizza in each option (using $\pi \approx 3,14$) and explain which of the two offers is better value for the customer.
A garden sprinkler rotates through a circular sector of $120^\circ$. If the jet of water reaches a distance of $6\text{ metres}$, calculate: a) The arc length of lawn…
A garden sprinkler rotates through a circular sector of $120^\circ$. If the jet of water reaches a distance of $6\text{ metres}$, calculate:
- a) The arc length of lawn that gets wet on the outer edge.
- b) The total area of lawn watered by the sprinkler.
(Use $\pi \approx 3,14$ and round to two decimal places).
Back to the beginning: The bicycle wheel and the basketball hoop are circumferences (only the outer edge is hollow), whereas the pizza is a circle (it has a filled interior surface, which is why you can eat it).