Answer:
9)5π in
10)104π ft²
11)7 in
12)rectangular pyramid
13)40.5 in³
14)256π/3 ft³
Step-by-step explanation:
9) Given Radius,r=12m
angle of sector ACB, Θ=75°=[tex]75\frac{\pi}{180}radians[/tex]
for given angle of sector, Θ the length of the arc will be [tex]r\theta[/tex]
⇒length of arc AB=[tex](12)(75\frac{\pi}{180})[/tex]
=[tex]5\pi[/tex] m
10) Given Radius,r=12 ft
angle of minor sector,Θ1=100°=[tex]100\frac{\pi}{180}=5\frac{\pi}{9}[/tex] radians
angle of major sector, Θ2=360°-100°=260°=[tex]260\frac{\pi}{180}=13\frac{\pi}{9}[/tex] radians
for a given angle of sector,Θ, the area of sector =[tex]\frac{r^{2}\theta}{2}[/tex]
⇒area of shaded region=area of major sector=[tex]\frac{12^{2}*(13\frac{\pi}{9})}{2}[/tex]
=[tex]\frac{144*13\pi}{18}=104\pi[/tex] ft²
11) Given area of circle,A=153.9 in²
but area of circle is given by [tex]\pi r^{2}[/tex] where r is the radius of the circle.
⇒[tex]\pi r^{2}=153.9[/tex]
⇒[tex]r^{2}=\frac{153.9}{\pi}=\frac{153.9}{3.14}=49.01[/tex]
⇒[tex]r=\sqrt{49.01}=7in(approx)[/tex]
12) The following figure is pyramid but since its base is a rectangular, its known as rectangular pyramid.
13) Given in cylinder:
radius,r=3 in
height,h=4.5 in
Volume of cylinder=[tex]\pi r^{2}h[/tex]
=[tex]\pi(3)^{2}(4.5)=40.5\pi[/tex] in³
14) Given diameter of sphere,d=8 ft
volume of sphere=[tex]\frac{4}{3}\pi r^{3}=\frac{\pi d^{3}}{6}=\frac{\pi(8)^{3}}{6}=\frac{256\pi}{3}[/tex] ft³
