A - actuary...........that is the answer
Answer:
270 miles
Step-by-step explanation:
45x2=90
90x3=270
Let C be the center of the circle. The measure of arc VSU is
, so the measure of the minor arc VU is
. The central angle VCU also has measure
.
Triangle CUV is isosceles, so the angles CVU and CUV are congruent. The interior angles of any triangle are supplementary (they add to 180 degrees) so
![m\angle VCU+2m\angle CUV=180](https://tex.z-dn.net/?f=m%5Cangle%20VCU%2B2m%5Cangle%20CUV%3D180)
![\implies m\angle CUV=\dfrac{180-(358-114x)}2=57x-89](https://tex.z-dn.net/?f=%5Cimplies%20m%5Cangle%20CUV%3D%5Cdfrac%7B180-%28358-114x%29%7D2%3D57x-89)
UT is tangent to the circle, so CU is perpendicular to UT. Angles CUV and VUT are complementary, so
![(57x-89)+(31x+3)=90](https://tex.z-dn.net/?f=%2857x-89%29%2B%2831x%2B3%29%3D90)
![\implies88x=176](https://tex.z-dn.net/?f=%5Cimplies88x%3D176)
![\implies x=2](https://tex.z-dn.net/?f=%5Cimplies%20x%3D2)
So finally,
![m\widehat{VSU}=2+114\cdot2=230](https://tex.z-dn.net/?f=m%5Cwidehat%7BVSU%7D%3D2%2B114%5Ccdot2%3D230)
degrees.
Vcylinder=hpir^2
Vsphere=(4/3)pir^3
Vcone=(1/3)hpir^2
Vcylinder=15*pi*5^2=375pi in^3
Vsphere=(4/3)*pi*6^3=288pi in^3
Vcone=(1/3)*15*pi*8^2=320pi in^3
greatest is Vcylinder at 375pi in^3
answer is A (cylinder)