The area of the sector is proportional to the angle of the central angle: area of the sector = angle of the central angle ------------------------------------ -------------------------------------------- area of the total circle total angle of the circle
Hi mister "youtubemathman" A cow is tethered to a post with a chain. The chain has a length of 4 meter. When the cow has eaten all the grass it can reach it has got 75% of a days meal. How long should the post be moved in order for the cow to reach the last 25%? Love your videos, keep up the good work. Regards and happy new year. spuncut
It's the same thing. In a technical field it's more likely to be said as " squared" than "square ". But then, in a technical field is more likely to be metres than feet.
@@gavindeane3670 I grew up during the time of 'the 'decimalization' of UK currency and 'metrification' in schools. As a result, I'm comfortable wih and still use both metric and imperial on a day to day basis; it's a bit akin to speaking two languages. 🙂
You could argue that, properly, "feet squared" should be preferred over "square feet" but they're literally the same thing. The ONLY way they can be used is interchangeably.
Circular areas AND I can explain what a radian is? Sweet! In order to get the area of a section of a circle, it is helpful to know that the area of a whole circle is: A = pi * r^2 Since the section we are focusing on is a slice of the circle, its area is simply a percentage of the above, defined by the angle formed around the center by this slice. In this case, the angle measures is 2*pi/5 radians. I see you have a confused look on your face when I said “radians”. You may be used to a circle having 360 degrees, but as useful as 360 degrees are, this is ultimately a contrived measurement. If there is one angle measure that is natural to the circle itself is the radian. A radian is defined as the angle measure of a circle at its center that captures an arc of the edge that is equal to its radius (about 57 degrees and change). So how many radians would a full circle be? Since a full circle is its entire circumference, we get that a full circle has a measure of 2*pi radians. Any full circle will be 2*pi radians around. So, we have an angle measure of 2*pi/5 radians. How much of the circle is that? Well, divide it by 2*pi: (2 * pi / 5) / (2 * pi) (2 * pi / 5) * (1 / (2 * pi)) (1 / 5) * (1 / 1) 1 / 5 So we are dealing with 1/5th of the area of this circle. So with its radius, we just need to calculate its whole area, then divide it by 5. A = (pi * r^2) / 5 = (pi * 7.2 ft ^2) / 5 = (51.84 * pi) sq ft / 5 A = 10.368 * pi sq ft Given pi is about 3.14, that gives us about 32.5 square feet. Any questions? Addendum: 32.6, oh, right. Honestly, I’d just leave it with pi.
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The area of the sector is proportional to the angle of the central angle:
area of the sector = angle of the central angle
------------------------------------ --------------------------------------------
area of the total circle total angle of the circle
Happy New year 🎉 ✨
Happy New Year !!!!
happy new year
(πr²)/5
Tuesday, 31 December 2024, 22:17 PM
gegeven : central angle θ = 2π/5
Radius r = 7.2 ft
gevraagd : oppervlakte sector
oplossing :
Area(sector) = ½θr²
A = ½· 2π/5 · [7.2]²
A = π/5 · 51.84
A = 51.84/5 · π
A = 10.368π ft²✅
Hi mister "youtubemathman"
A cow is tethered to a post with a chain.
The chain has a length of 4 meter.
When the cow has eaten all the grass it can reach it has got 75% of a days meal.
How long should the post be moved in order for the cow to reach the last 25%?
Love your videos, keep up the good work.
Regards and happy new year.
spuncut
2 . pi / 5 = 360° / 5 so A = pi . r² / 5 = pi . (7.2)² / 5 ~ 32.6 ft²
In English (UK) we say the unit of area as "Square Feet" not feet squared ... But I also accept that 'Math' can be quite 'pedantic' 🤗
More semantic than pedantic. I answered square feet also and I'm not British.
It's the same thing. In a technical field it's more likely to be said as " squared" than "square ". But then, in a technical field is more likely to be metres than feet.
@@gavindeane3670 I grew up during the time of 'the 'decimalization' of UK currency and 'metrification' in schools. As a result, I'm comfortable wih and still use both metric and imperial on a day to day basis; it's a bit akin to speaking two languages. 🙂
Area of sector = ½ r² θ (θ in radians)
"Feet squared" and "square feet" should NOT be used interchangeably.
What’s the difference between feet squared and square feet?
Please explain.
Please explain
Yeah, don't leave us hanging. :)
You could argue that, properly, "feet squared" should be preferred over "square feet" but they're literally the same thing. The ONLY way they can be used is interchangeably.
👌
woo hoo got 32.57 sq ft 2pi = radians of a circle arera = pi r ^2 = 3.141 X 7.2^2 = 162.83 / 5 (from your question)
= 32.57 thanks for the fun.
Circular areas AND I can explain what a radian is? Sweet!
In order to get the area of a section of a circle, it is helpful to know that the area of a whole circle is:
A = pi * r^2
Since the section we are focusing on is a slice of the circle, its area is simply a percentage of the above, defined by the angle formed around the center by this slice. In this case, the angle measures is 2*pi/5 radians.
I see you have a confused look on your face when I said “radians”. You may be used to a circle having 360 degrees, but as useful as 360 degrees are, this is ultimately a contrived measurement. If there is one angle measure that is natural to the circle itself is the radian. A radian is defined as the angle measure of a circle at its center that captures an arc of the edge that is equal to its radius (about 57 degrees and change). So how many radians would a full circle be? Since a full circle is its entire circumference, we get that a full circle has a measure of 2*pi radians. Any full circle will be 2*pi radians around.
So, we have an angle measure of 2*pi/5 radians. How much of the circle is that? Well, divide it by 2*pi:
(2 * pi / 5) / (2 * pi)
(2 * pi / 5) * (1 / (2 * pi))
(1 / 5) * (1 / 1)
1 / 5
So we are dealing with 1/5th of the area of this circle. So with its radius, we just need to calculate its whole area, then divide it by 5.
A = (pi * r^2) / 5
= (pi * 7.2 ft ^2) / 5
= (51.84 * pi) sq ft / 5
A = 10.368 * pi sq ft
Given pi is about 3.14, that gives us about 32.5 square feet.
Any questions?
Addendum: 32.6, oh, right. Honestly, I’d just leave it with pi.