MHB Find the area of the shaded region in terms of pi.

  • Thread starter Thread starter Etrujillo
  • Start date Start date
  • Tags Tags
    Area Pi Terms
AI Thread Summary
The area of a full circle is calculated using the formula πr². For a sector, the area is determined by the fraction of the circle's angle, leading to the formulas (120/360)(πr²) and (270/360)(πr²). With a radius of 12 meters, the area of the first sector is confirmed as 12π, while the area of the second sector is calculated as 108π. The final confirmation of the area for the second sector is expressed as A=(1/2)(12 m)²(3π/2)=108π m². The calculations for both sectors are verified as correct.
Etrujillo
Messages
9
Reaction score
0
So far i have.

12) area of full circle is πr²
area of sector is (120/360)(πr²) or 12π

13) same
area is (270/360)(πr²)

Am i correct?

View attachment 8706
 

Attachments

  • 20181204_093323-4.jpg
    20181204_093323-4.jpg
    13.8 KB · Views: 137
Mathematics news on Phys.org
#12 is correct ... finish #13
 
Im assuming 12m is the radius so \frac{270}{360}pi×12squared=108 pi
Am i correct?
 
$$A=\frac{1}{2}r^2\theta=\frac{1}{2}(12\text{ m})^2\frac{3\pi}{2}=108\pi\text{ m}^2\quad\checkmark$$
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Similar threads

MHB Find the areas of segment in circle
Replies
1
Views
2K
MHB ASVAB circle and inscribed rectangle area problem
Replies
6
Views
1K
MHB Area of Triangle Shaded Region
Replies
5
Views
2K
MHB Find the area of sector in a circle in terms of pi. (Geometry)
Replies
3
Views
1K
MHB Find the exact shaded area of the region in 4 overlapping circles
Replies
1
Views
3K
MHB Find the area of the shaded region
Replies
2
Views
1K
B A Simpler Way to Find the Shaded Area?
Replies
1
Views
2K
I Equation to graph a sine wave that acts like a point on a unit circle
Replies
8
Views
2K
I Why is the area of a circular cap on a sphere not equal to πr^2?
Replies
11
Views
7K
MHB Finding the Area of Shaded Part
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top