Question

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Answer 1

9)5π in

10)104π ft²

11)7 in

12)rectangular pyramid

13)40.5 in³

14)256π/3 ft³

Explanation:

9) Given Radius,r=12m

angle of sector ACB, Θ=75°=
`75(\pi)/(180)radians`

for given angle of sector, Θ the length of the arc will be
`r\theta`

⇒length of arc AB=
`(12)(75(\pi)/(180))`

=
`5\pi` m

10) Given Radius,r=12 ft

angle of minor sector,Θ1=100°=
`100(\pi)/(180)=5(\pi)/(9)` radians

angle of major sector, Θ2=360°-100°=260°=
`260(\pi)/(180)=13(\pi)/(9)` radians

for a given angle of sector,Θ, the area of sector =
`(r^(2)\theta)/(2)`

⇒area of shaded region=area of major sector=
`(12^(2)*(13(\pi)/(9)))/(2)`

=
`(144*13\pi)/(18)=104\pi` ft²

11) Given area of circle,A=153.9 in²

but area of circle is given by
`\pi r^(2)` where r is the radius of the circle.

⇒
`\pi r^(2)=153.9`

⇒
`r^(2)=(153.9)/(\pi)=(153.9)/(3.14)=49.01`

⇒
`r=√(49.01)=7in(approx)`

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=
`\pi r^(2)h`

=
`\pi(3)^(2)(4.5)=40.5\pi` in³

14) Given diameter of sphere,d=8 ft

volume of sphere=
`(4)/(3)\pi r^(3)=(\pi d^(3))/(6)=(\pi(8)^(3))/(6)=(256\pi)/(3)` ft³