1. A circle of diameter 30 cm has a sector of 65 degrees removed. What is the perimeter and surface area of the rest of the circle?
2. A circle of diameter 15 cm has part of a right-angled triangle overlapping it. One angle of the triangle, measuring 37 degrees, is at the dead centre of the triangle, and one side of length 25m, extends outward to the right angle.
What is the area of the triangle that is outside of the circle?
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solution 1
ReplyDeletediameter of the circle = 30cm
angle of sector removed = 60 degrees
area of circle = pie*r^2
area of sector = @/360* pie*r^2
to find the surface area of the remainder of the circle we must find the area of the sector and subtract it from the area of the whole circle.
area of the whole circle = pie * r^2
=706.8 cm^2
area of the sector = @/360*pie * r^2
= 117.8
remaining surface area = 706.8 - 117.8
=589cm^2
preimeter of whole circle= 2pie * r
= 94.2cm
perimeter of sector = @/360* 2pie*r
=15.7cm
perimeter of the remainder of the circle
=94.2 - 15.7
= 78.5cm
solution 2
ReplyDeletei think this question is worded wrongly
- i think the triangle surpose to be measured in centimeters and not in meters
- it supposed to be the dead center of the circle and not the triangle.
solution to the problem with the mistakes corrected.
first we need to find the area of the triangle.
we can use trigs to find the the heightof the triangle
so
tan@ = opp/adj
opp = adj tan@
= 25 tan@
= 18.8cm
area of the triangle = (b*h)/2
= (25*18.8)2
= 235cm^2
next we find the area of the sector
area of the sector = @/360 * pie*r^2
= 18.2cm^2
area of triangle outside of the circle
= 235-18.2
= 216.6cm^2
How`to`find`the`area`&`perimeter`of`sector?
ReplyDeleteWell`first`we`must`consider`what`is`a`secor`
A`Sector`of`a`circle`is`any`part`bounded`by
two`radii`and`an`arc`(part`of`a`circle)
The`AREA`&`PERIMETER`is`given`by:
Area=:(angle/360)*pie*radius^2
Perimeter=(2*r)+[(x*pie*radius)/180]
note`x`is:`angle`of`sector/360
so`knowing`this`we`will`attempt`Question`1
1. A circle of diameter 30 cm has a sector of 65 degrees removed. What is the perimeter and surface area of the rest of the circle?
Perimeter`of`circle:2*pie*radius
so
P=2*pie*15
P=94.25cm^2
Perimeter`of`sector:
Perimeter=(2*r)+[(x*pie*radius)/180]
note`x`is:`angle`of`sector/360
so
x=65/360=0.181
r=15
P=(2*15)+[(0.181*pie*15)/180)]
P=30+[8.53/180]
P=30+0.047
P=30.05m^2
To`get`the`perimeter`of`the`restof`the`circle
you`minus`Perimeter`of`circle`and`the`sector
so
Perimeter`of`the`rest`of`the`circle`is:
P=P1-P2
P=94.25-30.05
P=64.2cm^2
Answer`for`remaining`perimeter`is:63.2cm^2
We`will`work`out`the`area`now
area`of`circle`is:pie*radius^2
A=pie*15^2
A=706.9cm^2
area`of`sector`is:(angle/360)*pie*radius^2
A=(65/360)*706.9
A=0.181*706.9
A=128cm^2
We`can`now`get`the`area`of`the`remaining`circle`by`subtracting`the`2`areas
so
Area`remaining`:A1-A2
A=706.9-128
A=579cm^2
Answer`for`remaining`Area:579cm^2
shotta
ReplyDeletei`tink`Q2`have`an`error`also
but`i'll`try`it`using`your`method
Sorry, question 2 should have read:
ReplyDelete2. A circle of diameter 15 cm has part of a right-angled triangle overlapping it. One angle of the triangle, measuring 37 degrees, is at the dead centre of the circle, and one side of length 25cm, extends outward to the right angle.
What is the area of the triangle that is outside of the circle?
weezy, perimeter is not measured in cm^2 just cm
ReplyDeleteThis comment has been removed by the author.
ReplyDeletemiss please check the two solutions for question 1 and see who one is correct!!
ReplyDelete