A hollow cylinder has solid hemisphere in one end (bottom) and on the other end (top), it is open. The cylinder is filled with water upto the height 10 cm. Find the volume of water if the common diameter is 8 cm. [Answer in rational form]. Also, if the top end is covered with a plate and it is reversed, then find height of the water now.

Question

mathhelper · Answer

ambigious:
1. "upto the height 10 cm"
does the height of 10 cm include the height of the hemisphere, or is it
10 cm above the hemisphere part ?

2. If the hemisphere is solid, it can't hold any water, I will assume it holds water

I will conclude it is 4 cm of hemisphere + 6 cm of cylinder
Vol = (1/2)(4/3)π (4^3) + π(4^2)(6) = 416/3 π cm^3

If turned upside down:
416/3 π = π(4^2)(h)
416/3 = 16h
h = 26/3

the water height would be 26/3 cm

Make corrections to your post if I did not interpret it correctly.

Kaur · Answer

@mathhelper To calculate h , Do we need to subtract volume of cylinder - volume of hemisphere Or your way is right?????