## Circles - Due 14th June, 23:59 HOL time.

Please send all your work to hol.mathematics@gmail.com.

Send Homework and Extra Credit together or separately, whichever is easier for you.

Please put "Circles - HOL ID" in the subject line.

Remember to include your HOL username, ID and House in the main body of your email.

Do not send attachments as they will not be opened.

Send Homework and Extra Credit together or separately, whichever is easier for you.

Please put "Circles - HOL ID" in the subject line.

Remember to include your HOL username, ID and House in the main body of your email.

Do not send attachments as they will not be opened.

## Homework

__Parts of a circle - 10 points, 2 points each__In the picture below there are 5 parts of a circle to identify: blue, green, red and pink lines and yellow section. Tell me their mathematical names.

**Circumference Questions - 10 points***2 points per question and 2 points for including the correct units - they're not all cm this time around!*

You do not need to include your working out but if you want to send it with your answers it will help me to identify any errors or misunderstandings you have.

**Area Questions - 10 points***2 points per question and 2 points for including the correct units - they're not all cm squared for this exercise!*

You do not need to include your working out but if you want to send it with your answers it will help me to identify any errors or misunderstandings you have.

## Extra Credit

**Research Assignment - 10 points**Although I mentioned the Greeks in the lesson when discussing pi, the symbol wasn't used to represent the relationship between diameter and circumference until a much later date. Find out who first used the pi symbol to stand for 3.14... and when this occured. Tell me a little about how it became commonly used by mathematicans. Write about your findings in at least 150 words.

**Problem Solving - 20 points, 4 points each**Give the correct units with your answers. You are welcome to include your working out with your solutions but this isn't required for full points.

1. A bicycle wheel of diameter 80cm makes 20 complete rotations as the bicycle moves forward in a straight line.

(a) Find the circumference of the wheel.

(b) Work out how far the bicycle moves forward in total.

2. A lawn sprinkler sprays water 5 feet in every direction as it rotates. What is the area of the sprinkled lawn?

3. A semi circle has a radius of 15 cm. Calculate the area of the semi circle.

4. A pizza has a diameter of 18 inches. The pizza is cut into eight pieces. Find the area of each piece.

5. An asteroid hit the earth and created a huge circular crater. Scientists measured the distance around the edge of the crater as 78.5 miles. What is the diameter of the crater to the nearest mile?