SURFACE AREAS
AND VOLUMES
1 cm
Q. A solid is in the shape of a cone standing on a hemisphere
with both their radii being equal to 1 cm and the height of the
cone is equal to its radius. Find the volume of the solid in terms
of π.
Volume of solid =
The entire solid is made up
of a cone and a hemisphere
What is the formula to find volume of a hemisphere?
What is the formula to find volume of a cone?
Volume of cone (V1) +
Volume of hemisphere (V2)
✔
✔
Sol.
✔
1 cm
Volume of hemisphere (V2)
Now
Volume of cone (V1)
=
×
πr2h
h = r = 1cm.
=
×
π
×
1
×
1
×
1
=
π
Volume of hemisphere (V2)
=
×
πr3
=
×
π
×
1
×
1
×
1
=
π
1
3
1
3
1
3
2
3
2
3
2
3
cm3
cm3
∴
Volume of cone (V1)
∴
1 cm
1 cm
Volume of solid =
Volume of cone (V1) +
Volume of hemisphere (V2)
Sol.
Q. A solid is in the shape of a cone standing on a hemisphere
with both their radii being equal to 1 cm and the height of the
cone is equal to its radius. Find the volume of the solid in terms
of π.
Volume of the solid
=
V1
=
π
+
π
+
V2
Volume of the solid
=
π cm3
1
3
2
3
∴
=
3
π
+
2
π
=
3
3
π
=
π cm3
1 cm
1 cm
Sol.
Volume of solid =
Volume of cone (V1) +
Volume of hemisphere (V2)
Q. A solid is in the shape of a cone standing on a hemisphere
with both their radii being equal to 1 cm and the height of the
cone is equal to its radius. Find the volume of the solid in terms
of π.