Circles 4
Student Quiz - Circles 4
Use this 9 question quiz for some quick fire practise and revision on the topic of circles. The questions will ask you about the null and alternate hypotheses, 1 and 2 tailed tests and ask you to calculate p-numbers and use them to conclude your test for different significance levels. Do these on the go on your mobile or at your desk with a pen and paper by your side to help you. Answer the questions as best you can and then see how you did and read the solution notes included. Make a note of anything you misunderstood and revisit this quiz and many others as often as you like!
The Area of a sector formula is given by, \(A=\frac { \theta }{ 360 } \times \pi { r }^{ 2 }\). Rearrange this formula to write \(\theta\) in terms of \(A\) and \(r\).
Given that \(\theta\) is divided by 360°, we must multiply both sides by 360°. Also, since we are multiplying \(\theta\) by \(\pi{r}^2\), we must divide both sides by \(\pi{r}^2\). Essentially we are conducting the inverse operations when rearranging.
Which formulae below find the circumference of a circle, C, with radius, r, and diameter, d?
See answers.
A garden sprinkler is set at an angle of 160° and a spray distance of 4 metres. Find the area of grass that the sprinkler covers, leaving your answer to 3 significant figures. Do not include units.
Using the area of a sector formula:
\(A=\frac { 160° }{ 360° } \times \pi \times { 4 }^{ 2 }=22.3{ m }^{ 2 }\)
Find the area of a sector of a circle with radius 8 cm and central angle 10°. Give your answer to 3 significant figures. Do not include units.
The area of the sector is given by:
\(A=\frac { 10° }{ 360° } \times \pi \times { 8 }^{ 2 }=5.5851{ cm }^{ 2 }=5.59{cm}^2\)
Find the total perimeter of the shape below, giving your answer to 3 significant figures. Do not include units.
There are a number of ways to do this, one way being to find the interior angle of the sector, which is 320°, and then utilize the arc length formula to obtain 39.0954 cm. To then find the total perimeter, we must add 14 cm for the two radii, giving 53.1 cm to 3 significant figures.
Find the arc length of a sector with radius 6cm and a central angle of 120 degrees. Give your answer in terms of \(\pi\).
Using the formula for the arc length of a sector:
\(A=\frac { 120° }{ 360° } \times 2\times \pi \times 6=\frac { 1 }{ 3 } \times 12\pi =\frac { 12\pi }{ 3 } =4\pi \) cm
A semi-circlular logo has a radius of 10cm. Find the area of the logo, giving your answer to 1 decimal place.
We could use the formula for the area of a sector, with the angle, \(\theta\), being 180 degrees. However, it may be more efficient to use the formula for the area of a circle and then divide that area by 2 to get the area of the semi-circle.
\(A=\frac { \pi \times { 10 }^{ 2 } }{ 2 } =157.0796{ cm }^{ 2 }=157.1{ cm }^{ 2 }\)
If the area of a sector is \(50{c m }^{ 2 }\) and the central angle is 45 degrees, find the radius of the sector.
Using the formula for the area of a sector:
\(50=\frac { 45° }{ 360° } \times \pi { r }^{ 2 }\)
Dividing both sides by \(\frac { 45° }{ 360° }\) and by \(\pi\):
\({r}^2=127.324...\)
\(\therefore \quad r=11.3cm\)
Find the length of a cicular arc which has a radius of 5 cm and a central angle of 30°.
Using the arc length formula:
\(l=\frac { 30° }{ 360° } \times 2\times \pi \times 5=2.62\quad cm\)