A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on
a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water
such that it touches the bottom. Find the volume of water left in the cylinder, if the radius
of the cylinder is 60 cm and its height is 180 cm.
Answers
Step-by-step explanation:
Volume of Water left in Cylinder = 1131428.57 cm³
Step-by-step explanation:
Given: Height of Cone, h = 120 cm and Radius of Cone, r = 60 cm
Radius of Hemisphere, r = 60 cm
Height of Cylinder, H = 180 cm and Radius of Cylinder, r = 60 cm
To find: Volume of water left in cylinder
Volume of water left in cylinder = volume of cylinder - ( volume
of cone + volume of hemisphere )
= \pi r^2H-(\frac{1}{3}\pi r^2h+\frac{2}{3}\pi r^3)πr
2
H−(
3
1
πr
2
h+
3
2
πr
3
)
= \pi r^2(H-(\frac{1}{3}h+\frac{2}{3}r))πr
2
(H−(
3
1
h+
3
2
r))
= \frac{22}{7}\times60^2(180-(\frac{1}{3}\times120+\frac{2}{3}\times60))
7
22
×60
2
(180−(
3
1
×120+
3
2
×60))
= \frac{22}{7}\times3600(180-(40+40))
7
22
×3600(180−(40+40))
= \frac{22}{7}\times3600\times100
7
22
×3600×100
= 1131428.57 cm³
Therefore, Volume of Water left in Cylinder = 1131428.57 cm³