SURFACE AREAS
AND VOLUMES
1.4
Sol.
2
Radius =
10 m
1.4 m
55 m
14 m
h
Volume of cylinder =
Volume of cuboid
What is shape of well ?
Cylinder
Q. A 10 m deep well of diameter 1.4 m is dug up in a field and the earth
from digging is spread evenly on the adjoining field. The length and
breadth of that field are 55 m and 14 m resp. Find the thickness of the earth layer.
Breadth = 14 m
The entire earth dug completely
fills the cuboidal field
π r2 H
l b h
✔
✔
✔
?
✔
?
What is the formula to find volume of cuboid ?
What is the formula to find volume of cylinder?
Volume of the
cylindrical well
i.e. Volume of the
cuboid
What is relation between
volume of cylindrical well
and volume of cuboid?
They are equal
m
Length = 55 m
How much earth did we obtain
by digging the cylindrical well ?
Q. A 10 m deep well of diameter 1.4 m is dug up in a field and the earth
from digging is spread evenly on the adjoining field. The length and
breadth of that field are 55 m and 14 m resp. Find the thickness of the earth layer.
`
1
14
14
20
Volume of cylinder
=
Volume of cuboid
Let the height of the cuboid be h.
×
∴
×
10
=
55
×
14
×
×
h
×
∴
×
10
×
×
=
h
×
11
h
=
h
=
0.02 m
1.4
2
Thickness of the earth layer is 0.02 m.
1.4
2
14
20
22
7
1
55
1
50
m
∴
Radius =
1.4
2
Sol.
π
× r2
× H
=
l
× b
× h
22
7
Volume of cylinder =
Volume of cuboid
π r2 H
l b h
?
5
2
10
∴
∴
2