This is a horizontal cylindrical tank. I need to find the point on a dipstick th

Question

This is a horizontal cylindrical tank. I need to find the point on a dipstick that indicates when the tank is 3/8 full. This is the work I have so far, but when it comes to finding the roots of the equation, there is obviously a problem. I know I need to find an appropriate value for z that also makes h + m = 1.5. Any help you can provide, based on my already completed word, would be greatly appreciated!

Areaul oide) Team t to know when ton is 8 tal, so So, we can find has by subach, he area of ine under manate from the area Of the sector. CCTO le associated with the sector Area second- loºTY HE LCD - Do a charge against tsuna o, we dont 10 Camachonham 1-5 hal5-m and we can worked out to be

Explanation / Answer

We know the total height of the tank = 2R = 3 m

When the tank is 3/8 full, the height of water in the tank is = h = 3/8 X 3 = 9/8 m

We already know that h+m=1.5 m

=> m = 3/2 -9/8 = 3/8 m

=> 3/8 = 3/2 cos(z/2)

=>cos(z/2)=1/4

=>cos(z)=2cos^2(z/2)-1 = -7/8 (using cos2x identity)

=>Sin(z)=sqrt(1-cos^2(z))=sqrt(1-49/64)=sqrt(15/64)

=>Putting this value in the derived equation find the value of Z

I hope this will help :)

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