Given:
Radius = 14 ft
θ = 45°
To find:
Area of the shaded sector
Solution:
Area of the sector formula:
![$\text { area of sector }=\frac{\theta}{360^{\circ}} \times \pi r^{2}](https://tex.z-dn.net/?f=%24%5Ctext%20%7B%20area%20of%20sector%20%7D%3D%5Cfrac%7B%5Ctheta%7D%7B360%5E%7B%5Ccirc%7D%7D%20%5Ctimes%20%5Cpi%20r%5E%7B2%7D)
![$=\frac{45^\circ}{360^{\circ}} \times \pi \times 14^{2}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B45%5E%5Ccirc%7D%7B360%5E%7B%5Ccirc%7D%7D%20%5Ctimes%20%5Cpi%20%5Ctimes%2014%5E%7B2%7D)
![$=\frac{1}{8} \times \pi \times 196](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B1%7D%7B8%7D%20%5Ctimes%20%5Cpi%20%5Ctimes%20196)
ft²
The area of the shaded sector of a circle is 24.5π ft².
Answer:
x=-5.25
y=13.75
Step-by-step explanation:
5x+3(-3x-2)=15
5x+-9x+-6=15
-4x+-6=15
-4x+-6+6=15+6
-4x=21
Given:
Consider the below figure attached with this question.
To find:
The surface area of this solid prism.
Solution:
The surface area of this solid prism is
![A=P\times h+2B](https://tex.z-dn.net/?f=A%3DP%5Ctimes%20h%2B2B)
Where, P is the perimeter of the base, B is the area of the base and h is the height of the prism.
Perimeter of the base is:
![P=6+8+10](https://tex.z-dn.net/?f=P%3D6%2B8%2B10)
![P=24](https://tex.z-dn.net/?f=P%3D24)
Area of the base is:
![B=\dfrac{1}{2}\times base\times height](https://tex.z-dn.net/?f=B%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%20base%5Ctimes%20height)
![B=\dfrac{1}{2}\times 8\times 6](https://tex.z-dn.net/?f=B%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%208%5Ctimes%206)
![B=24](https://tex.z-dn.net/?f=B%3D24)
Putting
and
in the formula for area, we get
![A=(24)\times 9+2(24)](https://tex.z-dn.net/?f=A%3D%2824%29%5Ctimes%209%2B2%2824%29)
![A=216+48](https://tex.z-dn.net/?f=A%3D216%2B48)
![A=264](https://tex.z-dn.net/?f=A%3D264)
Therefore, the surface area of the given prism is 264 m².