Circle
1.Primary 7 are making medieval hats as part
of their History project.
A few of the girls decide to make a hat like
the one shown , which consists of a cone
shaped body made of card with a ribbon
attatched to the top.
The sector of card used to make the cone is
cut from a square piece of card of side 40 cm
as shown.
If the angle at the centre of the sector is 250o,
calculate the percentage of card wasted, to
the nearest percent.
5R
2.KENNOLAUT, the dog food specialists, have recommended that dogs should
drink at least three times the volume of food they consume. To promote this the
company have designed a new feeding dish with two sections, as shown in the
diagrams below.
side and above view
top view
The larger section is for water and the smaller section is for food.
The dish is cylindrical in shape with a radius of 15cm.
The dividing strip is 26cm long.
If filled to capacity will the dish satisfy the company’s recommendation?6R
3. A large boardroom table is in the shape of a rectangle with a circle segment at both ends, as shown in the diagram below.
The rectangle at the centre measures 6 metres by 35 metres.
AC and BC are radii of the circle and angle ACB is 120o.
(a)Show that AC, the radius of the segment, is 202m correct to 3 significant figures.
3R
(b)To sit comfortably at this table it is estimated that an average person requires 80
cm of table edge. How many people can sit comfortably at the table described
above? 4R
4. Circle A has a circumference of centimetres and circle B has a circumference
of centimetres.
Calculate the difference in size between the radius of circle A and the radius of
circle B. 3R
5.The pair of compasses shown in the diagram
oppositeis used to draw a complete circle.
It is 86 centimetres from the top of the compass
to the jagged point and 89 centimetres from the top
to the pencil point. The angle between the two arms
is 38o.
Calculate the circumference of the circle.
5R
6.The diagram below shows part of a football pitch designed for under 12’s.
The penalty spot O is 8 metres from the goal line, and the line AB is 11 metres from the goal line.
A circular arc, with centre O and radius 6 metres is marked.
Calculate the length of the arc AB to the nearest metre.5R
7.The area of the sector shown is 589 cm2.
Calculate the size of the angle marked xº3R
8.A metal strip has been moulded into an arc of a circle of radius 155 centimetres
which subtends an angle of 82o at the centre of the circle as shown in the diagram
below.
The samestrip of metal has now been remoulded to form an arc of a circle of
Radius210 centimetres as shown.
Calculate the size of x, the angle now subtended by the metal strip. 4R