An open metal bucket is in the shape of a frustum of a cone, mounted on a hollow
cylindrical base made of the same metallic sheet. The diameters of the two circular
ends of the bucket are 42 cm and 28 cm the total vertical height of the bucket is 30 cm
and that of the cylindrical base is 6 cm. Find the area of the metallic sheet is used to
make the bucket, where we do not take into account the handle of the bucket. Also,
find the volume of the water the bucket can hold.
Answers
Answer:
Step-by-step explanation:Area of metallic sheet used=CSA of frustum+CSA of cylinder +CSA of Base
CSA of frustum,
Diameter of bigger circular end=45cm
Radius=45/2=22.5cm
Diameter of smaller circular end=25cm
Radius=25/2=12.5cm
Height of the frustum=Total height of the bucket−Height of the circular base
40−6=34cm
Slant Height=
h
2
+(r
1
2
−r
2
)
2
=
34
2
+(22.5−(2.5)
2
)
=
1156+(10)
2
=
1256
Slant height=35−44cm
CSA of frustum=π(r
1
+r
2
)l=
7
22
(22.5+12.5)35.44
=
7
22
×35×35.44
=3898.4cm
2
Area of circular base
Base is a circular part with radius 25/2
Area of circular base=πr
2
=
7
22
×12.5×12=491.07cm
2
CSA of cylinder=2πrh=2×
7
22
×12.5×7=471.428
Area of metallic sheet used=3989.4+491.07+471.428
=4860.898cm
2
.