1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# A solid consisting of a right cone standing on a hemisphere is placed upright in a right circular cylinder full of water and touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60cm and its height is 180cm, the radius of the hemisphere is 60cm and height of the cone is 120cm, assuming that the hemisphere and the cone have common base.

Open in App
Solution

## For the cylinder we haveRadius of the base=r=60cmHeight =h=180cmVolume of water that the cylinder contains =V=πr2h={π×602×180}cm3For conical part, we haveRadius of the base =r=60cmHeight =h1=120cmVolume of conical part V1=13πr2h1=13π×602×120cm3={π×602×40}cm3For hemispherical part, we haveRadius =r=60cmVolume of the hemisphere V2={23π×603}cm3⇒V2={2π×602×20}cm3=(40π×602)cm3Hence volume of the water left out in the cylinder⇒V=V1−V2={π×602×180−π×602×40−40π×602}cm3=π×602×{180−40−40}cm3=227×3600×100cm3=22×36700m3=1.1314m3

Suggest Corrections
2
Join BYJU'S Learning Program
Related Videos
Volume of of Combination Solids
MATHEMATICS
Watch in App
Join BYJU'S Learning Program