a wooden solid cylinder has a radius 4 cm and height 7 cm . to increase its weight a conical hole is drilled in the cylinder and is completelly filled with a metal. the conical hole has a radius 3/2 cm and height is 3 cm . calculate the ratio of the volume of the wood to the volume of the metal in the solid
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A metallic cylinder has radius 3cm and height 5cm. It is made of metal A. To reduce its weight, a conical hole is drilled in the cylinder, as shown and it is completely filled with a lighter metal B. The conical hole has a radius of 3/2cm and its depth is 8/9cm. Calculate the ratio of the volume of the metal A to the volume of the metal B in the solid.
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Volume of metal B=
3
1
πr
1
2
h
1
=
3
1
π(
2
3
)
2
(
9
8
)=
3
2π
Volume of metal A=πr
2
h−
3
1
πr
1
2
h
1
=
3
π
(3r
2
h−r
1
2
h
1
)
=
7×3
22
(3×9×5−
4
9
×89)=
21
22
(135−2)=
21
22×133
=139.33 cm
3
ratio =
2π
139.33×3
=
3.14
209
=
π
209
=
22
209×7
=
2
133
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