SURFACE AREAS
AND VOLUMES
and Hemisphere
120 cm
60 cm
60 cm
Q. 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.
180 cm
Volume of water left =
Volume of cylinder (V1) –
Volume of solid (V2)
What is the formula to find volume of cylinder?
π r2 h1
What is the formula to find volume of solid?
Vol. of cone
+
Vol. of hemisphere
What is the formula to find volume of cone?
πr2h2
1
3
What is the formula to find volume of hemisphere?
πr3
2
3
✔
✔
✔
✔
✔
The solid consists of a cone and a hemisphere
Sol.
=
π
×
(60)2
×
180
=
6,48,000π cm3
Vol. of cylinder (V1)
=
πr2h1
Vol. of solid (V2)
=
Vol. of cone
+
Vol. of hemisphere
=
πr2h2
+
πr3
=
πr2
(h2 + 2r)
1
3
1
3
2
3
120 cm
60 cm
180 cm
=
π
×
3600
×
180
Q. 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.
Volume of water left =
Volume of cylinder (V1) –
Volume of solid (V2)
π r2 h1
+
πr2h2
1
3
πr3
2
3
=
π
×
(60)2
×
120
1
3
+ (2
× 60)]
60 cm
∴ Vol. of cylinder (V1)
[
=
288000 π cm3
Vol. of water left
=
6,48,000π
–
2,88,000π
=
π
×
(60)2
×
[120 + (2 × 60)]
1
3
Sol.
=
π
×
3600
×
(120
1
3
Q. 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.
+ 120)
=
π
×
3600
×
240
1
3
=
1200
×
240
1200
=
V1
–
V2
×
π
3,60,000π cm3
∴Vol. of water left =
Vol. of solid (V2)
120 cm
60 cm
180 cm
60 cm
∴ Vol. of solid (V2)
V1= 648000π
Volume of water left =
Volume of cylinder (V1) –
Volume of solid (V2)
π r2 h1
+
πr2h2
1
3
πr3
2
3
Sol.
Q. 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.
Volume of water left =
Volume of cylinder (V1) –
Volume of solid (V2)
=
3,60,000π cm3
=
×
=
∴ Volume of water left in the cylinder is 1.131 m3
=
1.131 m3
36
100
22
7
792
100 × 7
Vol. of water left
=
π
m3
3,60,000
1000000
=
36
100
π
=
36 × 22
100× 7
=
113.14
100
120 cm
60 cm
180 cm
60 cm