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Circles, SM-Bank 055

A plane is circumnavigating the earth at the equator. It is cruising at a constant altitude of 10 kilometres above the earths' surface.

Given the earths' radius is approximately 6400 kilometres at the equator, calculate the distance, \(d\), that the plane has travelled after completing one lap of the earth.

Give your answer correct to the nearest whole kilometre.  (3 marks)

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\(40\ 275\ \text{km  (nearest whole kilometre)}\)

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\(\text{Radius of planes’ path}=6400+10=6410\ \text{km}\)

\(d\) \(=2\pi r\)
  \(=2\pi \times 6410\)
  \(=40\ 275.2178\dots\)
  \(=40\ 275\ \text{km  (nearest whole kilometre)}\)

 
\(\therefore\ \text{The distance the plane travels around the earth}\)

\(\text{at the equator is approximately }40\ 275\ \text{kilometres.}\)

Circles, SM-Bank 054

Given the earths' radius is approximately 6400 kilometres, calculate the distance, \(d\), around the earth at the equator. Give your answer correct to the nearest whole kilometre.  (2 marks)

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\(40\ 212\ \text{km  (nearest whole kilometre)}\)

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\(d\) \(=2\pi r\)
  \(=2\pi \times 6400\)
  \(=40\ 212.3859\dots\)
  \(=40\ 212\ \text{km  (nearest whole kilometre)}\)

 
\(\therefore\ \text{The distance around the earth at the equator is approximately }40\ 212\ \text{kilometres.}\)

Circles, SM-Bank 038

Evan rides his bike around a circular track with a radius of 150 metres.

He rides the track 5 days a week and wants to have ridden 230 kilometres by the end of the week.

What is the minimum number of laps, to the nearest whole lap, he must complete each day to achieve his target?  (3 marks)

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\(49\ \text{laps}\)

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\(\text{Total Distance}=230\ \text{km}=230\ 000\ \text{m}\)

\(\text{Total laps}\) \(=\dfrac{230\ 000}{C}\)
  \(=\dfrac{230\ 000}{300\pi}\)
  \(=244.037\dots\)

 

\(\text{Laps per day:}\) \(=\dfrac{244.037\dots}{5}\)
  \(=48.807\dots\)
  \(\approx 49\ \text{laps}\)

 
\(\therefore\ \text{Evan needs to ride }49\ \text{laps per day to achieve his goal}.\)

\(\Big[\text{Check:  }49\times 5\times 300\pi=230\ 907.06\ \text{m}=230.907\ \text{km}\Big]\)

Circles, SM-Bank 037 MC

A car tyre has a circumference of 120 cm.

Which of these is closest to the radius of the tyre?

  1. \(9.5\ \text{cm}\)
  2. \(19.1\ \text{cm}\)
  3. \(38.0\ \text{cm}\)
  4. \(753.6\ \text{cm}\)
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\(B\)

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\(C\) \(=2 \pi r\)
\(120\) \(=2\times \pi\times r\)
\(r\) \(=\dfrac{120}{2 \pi}\)
  \(=19.098\dots\)
  \(\approx 19.1\ \text{cm}\)

 
\(\Rightarrow B\)

Circles, SM-Bank 036 MC

A yoyo at the end of a string moves through a quarter circle arc, as shown below.

The string is 70 cm long.
 

 
The curved distance the yoyo has travelled is closest to

  1. \(80\ \text{cm}\)
  2. \(90\ \text{cm}\)
  3. \(100\ \text{cm}\)
  4. \(110\ \text{cm}\)
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\(D\)

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\(\text{Distance}\) \(=\dfrac{1}{4}\times 2\pi r\)
  \(=\dfrac{1}{4}\times 2\pi 70\)
  \(= 109.9557\dots\)
  \(\approx 110\ \text{cm}\)

\(\Rightarrow D\)

Circles, SM-Bank 035

Guerra slings a fire torch in a circle at the end of a 3 metre rope.
 

How far has the fire torch travelled after completing 15 circles?

Give your answer correct to the nearest whole number.  (2 marks)

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\(283\ \text{metres  (nearest whole number)}\)

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\(\text{Distance travelled in 1 revolution:}\)

\(C\) \(=2\pi r\)
  \(=2\times \pi\times 3\)
  \(= 18.8495\dots\)

 

\(\therefore\ \text{Distance travelled in }15\ \text{revolutions:}\)

\(=15\times 18.8495\dots\)

\(= 282.7433\dots\)

\(=283\ \text{metres  (nearest whole number)}\)

Circles, SM-Bank 034 MC

A wheel on a bicycle has a diameter of 530 mm.
 

 
The wheel turns 12 times.

Approximately how many metres has the bicycle travelled?

  1. \(6\ \text{m}\)
  2. \(20\ \text{m}\)
  3. \(40\ \text{m}\)
  4. \(399\ \text{m}\)
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\(B\)

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\(\text{Diameter}=530\ \text{mm}=0.530\ \text{m}\)   

\(\therefore\ \text{Distance}\) \(=12\times \text{circumference}\)
  \(=12\times \pi d\)
  \(=12\times \pi\times 0.530\)
  \(=19.9805\dots\)
  \(=20\ \text{m  (nearest m)}\)

\(\Rightarrow B\)

Circles, SM-Bank 021

Percy has a large shower head which has a diameter of 25.5 centimetres.

What is the circumference of the shower head in centimetres, correct to one decimal place?   (2 marks)
 
 

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\(80.1\ \text{cm}\ (1\ \text{d.p.})\)

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\(C\) \(=\pi d\)
  \(=\pi\times 25.5\)
  \(=80.110\dots\)
  \(=80.1\ \text{cm}\ (1\ \text{d.p.})\)

Circles, SM-Bank 033

Calculate the radius of a circle with a circumference of 870 metres, correct to the nearest ten metres.  (2 marks)

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\(140\ \text{m}\ (\text{nearest ten})\)

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\(C\) \(=2\pi r\)
\(870\) \(=2\pi r\)
\(r\) \(=\dfrac{870}{2\pi}\)
  \(=138.4648\dots\)
  \(=140\ \text{m}\ (\text{nearest ten})\)

Circles, SM-Bank 032

Calculate the radius of a circle with a circumference of 324 centimetres, correct to 2 decimal places.  (2 marks)

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\(51.57\ \text{cm}\ (2\ \text{d.p.})\)

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\(C\) \(=2\pi r\)
\(324\) \(=2\pi r\)
\(r\) \(=\dfrac{324}{2\pi}\)
  \(=51.5662\dots\)
  \(=51.57\ \text{cm}\ (2\ \text{d.p.})\)

Circles, SM-Bank 031

Calculate the diameter of a circle with a circumference of 109.8 metres, correct to 2 decimal places.  (2 marks)

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\(34.95\ \text{m}\ (2\ \text{d.p.})\)

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\(C\) \(=\pi d\)
\(109.8\) \(=\pi d\)
\(d\) \(=\dfrac{109.8}{\pi}\)
  \(=34.9504\dots\)
  \(=34.95\ \text{m}\ (2\ \text{d.p.})\)

Circles, SM-Bank 030

Calculate the diameter of a circle with a circumference of 24 centimetres, correct to 1 decimal place.  (2 marks)

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\(7.6\ \text{cm}\ (1\ \text{d.p.})\)

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\(C\) \(=\pi d\)
\(24\) \(=\pi d\)
\(d\) \(=\dfrac{24}{\pi}\)
  \(=7.639\dots\)
  \(=7.6\ \text{cm}\ (1\ \text{d.p.})\)

Circles, SM-Bank 029

Calculate the circumference of a circle with a radius of 1012 centimetres, correct to the nearest hundred.  (2 marks)

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\(6400\ \text{cm}\ (\text{nearest hundred})\)

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\(C\) \(=2\pi r\)
  \(=2\pi\times 1012\)
  \(=6358.5835\dots\)
  \(=6400\ \text{cm}\ (\text{nearest hundred})\)

Circles, SM-Bank 028

Calculate the circumference of a circle with a radius of 453 kilometres, correct to the nearest whole number.  (2 marks)

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\(2846\ \text{km}\ (\text{nearest whole number})\)

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\(C\) \(=2\pi r\)
  \(=2\pi\times 453\)
  \(=2846.2829\dots\)
  \(=2846\ \text{km}\ (\text{nearest whole number})\)

Circles, SM-Bank 027

Calculate the circumference of a circle with a diameter of 24.6 millimetres, correct to 0ne decimal place.  (2 marks)

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\(77.3\ \text{mm}\ \ (1\ \text{d.p.})\)

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\(C\) \(=\pi d\)
  \(=\pi\times 24.6\)
  \(=77.2831\dots\)
  \(=77.3\ \text{mm}\ \ (1\ \text{d.p.})\)

Circles, SM-Bank 026

Calculate the circumference of a circle with a diameter of 35 centimetres, correct to two decimal places.  (2 marks)

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\(109.96\ \text{cm}\ \ (2\ \text{d.p.})\)

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\(C\) \(=\pi d\)
  \(=\pi\times 35\)
  \(=109.9557\dots\)
  \(=109.96\ \text{cm}\ \ (2\ \text{d.p.})\)

Circles, SM-Bank 025

Calculate the circumference of the circle below correct to two decimal places.  (2 marks)

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\(653.45\ \text{cm}\ \ (2\ \text{d.p.})\)

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\(C\) \(=2\pi r\)
  \(=2\pi\times 104\)
  \(=653.4512\dots\)
  \(=653.45\ \text{cm}\ \ (2\ \text{d.p.})\)

Circles, SM-Bank 024

Calculate the circumference of the circle below correct to one decimal place.  (2 marks)

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\(44.0\ \text{cm}\ \ (1\ \text{d.p.})\)

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\(C\) \(=2\pi r\)
  \(=2\pi\times 7\)
  \(=43.9822\dots\)
  \(=44.0\ \text{cm}\ \ (1\ \text{d.p.})\)

Circles, SM-Bank 023

Calculate the circumference of the circle below correct to one decimal place.  (2 marks)

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\(38.3\ \text{m}\ \ (1\ \text{d.p.})\)

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\(C\) \(=\pi d\)
  \(=\pi\times 12.2\)
  \(=38.3274\dots\)
  \(=38.3\ \text{m}\ \ (1\ \text{d.p.})\)

Circles, SM-Bank 022

Calculate the circumference of the circle below correct to two decimal places.  (2 marks)

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\(15.71\ \text{m}\ \ (2\ \text{d.p.})\)

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\(C\) \(=\pi d\)
  \(=\pi\times 5\)
  \(=15.7079\dots\)
  \(=15.71\ \text{m}\ \ (2\ \text{d.p.})\)

Circles, SM-Bank 020

Use a calculator to evaluate \(2\large\pi r\) correct to 1 decimal place, when \(\large r\)\(=2.1\).  (2 marks)

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\(13.2\ (1\ \text{d.p.})\)

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\(2\pi r\) \(=2\times \pi\times 2.1\)
  \(=13.194\dots\)
  \(=13.2\ (1\ \text{d.p.})\)

Circles, SM-Bank 019

Evaluate \(5\large\pi\) using a calculator, giving your answer correct to 2 decimal places.  (1 mark)

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\(15.71\ (2\ \text{d.p.})\)

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\(5\pi\) \(=15.7079\dots\)
  \(=15.71\ (2\ \text{d.p.})\)