1. A goat is in a square fi eld that has a side length of 14 m. The goat is tied to the middle of a 14 m fence on one side with a 5 m rope. Find the percentage of the fi eld the goat can reach, to the nearest whole number.
2. Shown on the right is a running track. The two end sections are semicircular. Calculate the area inside the running track, to nearest whole number.
3. The semicircle and square shown on the right have the same area. Calculate the side length of the square.
4. Shown is a circular photo frame. The photo part has a radius of 14 cm. The frame is shaded in the diagram, and has a width of 5 cm.
Work out area of the frame. Leave your answer in terms of π .
5. Find the measure of the angles marked with the letters on the dartboards below.
(i) (ii) A A B
6. A circular building has a diameter of 50 metres.
5 m 14 m
Draw a scale drawing of the base of building using the scale factor of 1 : 500.
84 m 73 m 84 m
7. A circular base for a building measures 500 m in radius.
Using a compass, draw a scale diagram (using an appropriate scale) to represent the base of this building. Include the scale used in the diagram.
8. The diameter of the moon is 3·474 × 10 3
km. 10 m
5 cm 14 cm
(i) Write the diameter of the moon in decimal form (without scientifi c notation).
(ii) Assuming the moon is perfectly circular, draw a scale diagram of the moon using an appropriate scale.
9. The radius of Earth is 6 371 km.
(i) Write the diameter of Earth in scientifi c notation.
(ii) Assuming Earth is perfectly circular, draw a scale diagram of the Earth using an appropriate scale.
A
(iii) How many times is the diameter of Earth bigger than that of the moon? Give your answer correct to two decimal places.