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{circle(circ6)}

The circumference of a circle is $\\var{circ6}$m. Find the length of the radius of the circle.

[[0]] m

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{circle1(area5)}

The area of a circle is $\\var{area5}$m$^2$. Find the radius of the circle?

[[0]]m

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{circle1(area12)}

This circle has an area of $\\var{area12}$m$^2$. Calculate the circumference of this circle.

[[0]]m

First you need to find the radius of this circle.

{circle(per22)}

Calculate the area of a circle which has a circumference of $\\var{per22}$m.

[[0]] m$^2$

First you need to find the radius of this circle.

A steel plate is in the shape of a quadrant of a circle and has a radius of $\\var{r[2]}$m. Calculate the perimeter of this plate and the area of the segment.

Perimeter = [[0]]m

Area = [[1]]m$^2$

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A quadrant is a quarter of a circle. Its area is a quarter of the area of a full circle. Its perimeter is made up of a curved part (one quarter of the circumference of a circle) and two straight edges (each is a radius).

A sector of a circle makes an angle of $\\theta=\\var{sect} ^{\\circ}$ at the centre and has a radius of $r=\\var{rad}$cm. Calculate the area of the sector.

Area of sector = [[0]]cm$^2$

The formula for area of a sector is $ \\frac{\\theta}{360}\\times \\pi r^2$

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We need the following formulae, where $A =$ Area of circle, $r =$ radius, $C =$ circumference:

$A=\\pi r^2$

$C= 2\\pi r$

(a)

$C= 2\\pi r$

$r = \\frac{C}{2 \\pi} =\\frac{\\var{circ6}}{2 \\pi}= \\var{precround(ans8,2)}$m

(b)

$r=\\sqrt\\frac{A}{\\pi} = \\var{precround(ans7,2)}$m

(c)

First we find the radius:

$A=\\pi r^2$

$r=\\sqrt\\frac{A}{\\pi} = \\var{precround(r[0],2)}$m

Now we can find the circumference:

$C= 2\\pi r = 2\\pi \\times \\var{r[0]} = \\var{precround(ans1,2)}$m

(d)

First we find the radius:

$C= 2\\pi r$

$r = \\frac{C}{2 \\pi} =\\frac{\\var{per22}}{2 \\pi}= \\var{precround(r[1],2)}$m

Now we can find the area:

$A=\\pi r^2=\\pi \\times \\var{r[1]}^2 = \\var{precround(ans2,2)}$m$^2$

(e)

The perimeter of the quadrant is made up of a curved part and two straight edges.

The length of the curved part of the quadrant is $\\frac{1}{4}$ of the circumference of a circle.

Therefore curved length = $\\frac{1}{4}\\times C= \\frac{1}{4}\\times 2\\pi r = \\frac{1}{4}\\times 2\\pi\\times\\var{r[2]}$

Each straight edge is just a radius of the circle, so each has length $r=\\var{r[2]}$

Therefore the total perimeter is $ (\\frac{1}{4}\\times 2\\pi\\times \\var{r[2]}) + \\var{r[2]}+\\var{r[2]} = \\var{precround(ans3,2)}$m

The area of the quadrant is one quarter of the area of the whole circle.

So $A=\\frac{1}{4}\\pi r^2=\\frac{1}{4}\\pi\\times\\var{r[2]}^2=\\var{precround(ans4,2)}$m$^2$

(f)

The area of the sector is $\\frac{\\theta}{360}$ of the area of the whole circle.

$A=\\frac{\\theta}{360}\\pi r^2=\\frac{\\var{sect}}{360}\\pi \\times \\var{rad}^2 = \\var{precround(ans5,2)}$m$^2$

", "preamble": {"css": "", "js": ""}, "statement": "

Solve the following to two decimal places.

", "tags": [], "metadata": {"description": "

Circumference and area of a circle

rebelmaths

", "licence": "Creative Commons Attribution 4.0 International"}, "extensions": [], "type": "question", "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}