Question

John and Jane go for a run round the roundabout every dawn. They run 6 rounds and cover a distance of 2400 metres. What is the diameter of the roundabout

Answer 1

Step-by-step explanation:

ANSWER:-

Given:-

• John and Jane go for a walk around a roundabout
• They cover 2400 metres every day.
• They also take 6 rounds.

To find:-

The diameter of the roundabout

Concept:-

Perimeter and Area

Let's Do!

We need to know that:-

$\sf{Perimeter \ of \ Circle = 2 \times \pi \times r}$

We need not require the "6 rounds", it is additional and

often confusing.

$\sf{2400 = 2 \times 3.14 \times r}$

$\sf{\dfrac{2400}{2 \times 3.14} = r}$

$\sf{Radius = 382.16 \ metres}$

Now, we know Diameter is 2 times the Radius.

So, $\sf{Diameter = 382.16 \times 2 }$

$\sf{Diameter = 764.32 \ metres \ is \ the \ required \ answer.}$

Answer 2

Gɪᴠᴇɴ :

• John and Jane run 6 rounds in the roundabout.

• They cover a distance of 2400 m.

Tᴏ Fɪɴᴅ :

• The diameter of roundabout.

Cᴀʟᴄᴜʟᴀᴛɪᴏɴ :

✯ John and Jane run in the roundabout, that means they run in a circular path or they run on the circumference (perimeter) of the circular.

We know that,

↝ Circumference of a circle is,

$\red\bigstar\:\bigg\{\:\bf\purple{Circumference\:=\:2\:\pi\:r\:}\:\bigg\}\:\red\bigstar$

Where,

• Circumference = 2400 m

• r is the radius of the circular path.

➣ $\:\bf{2400\:=\:2\:\pi\:r\:}$

➣ $\:\bf{r\:=\:\dfrac{2400}{2\:\pi}\:}$

➣ $\:\bf{r\:=\:\dfrac{2400}{2\times{\frac{22}{7}}}\:}$

➣ $\:\bf{r\:=\:\dfrac{1200\times{7}}{22}\:}$

➣ $\:\bf{r\:=\:\dfrac{600\times{7}}{11}\:}$

➣ $\:\bf{r\:=\:\dfrac{4200}{11}\:}$

➣ $\:\bf{r\:=\:381.81\:m}$

We know that,

$\pink\bigstar\:\bigg\{\:\bf\blue{Diameter\:=\:2\times{r}\:}\:\bigg\}\:\pink\bigstar$

➙ $\:\bf{Diameter\:=\:2\times{381.81}\:}$

➙ $\:\bf\green{Diameter\:=\:763.63\:m}$

$\Large\tt{Therefore,}$

The diameter of the roundabout is 763.63 m.