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The diagram represents a solid frustum with base radius of 35cm and top radius of 21cm.The frustum is 22.5cm high and is made of a metal whose density is 4g/cm3. Taking π = 22/7
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asked
Aug 16, 2021
in
Mathematics Form 2
by
anony mous
The diagram represents a solid frustum with base radius of 35cm and top radius of 21cm.The frustum is 22.5cm high and is made of a metal whose density is 4g/cm
^{3}
. Taking π =
^{ 22}
/
_{7}
Calculate;
The volume of the metal that makes the frustum.
The mass of the frustum.
The frustum is melted in down and recast into a solid cube in the process 20% of the metal is lost. Calculate to 2d.p the length of each side of the cube.
volume of solids
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1
Answer
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votes
answered
Aug 16, 2021
by
anony mous
h
=
21
h+22.5 35
35h = 21(h + 22.5)
35h − 21h = 472.5
14h − 472.5
h =
472.5
14
h=33.75
∴ vol of frustum =
^{1}
/
_{3}
^{π}
(R
^{2}
H − r
^{2}
h)
^{1}
/
_{3}
× 3.14(35
^{2}
× 56.25 − 21
^{2}
× 33.75)
^{1}
/
_{3}
× 3.14(68906.25 − 14883.75)
=56543.55cm
^{3}
Mass = D × V
= 56543.55 × 4 = 22174.2g
^{80}
/
_{100}
× 56543.55 = 45234.84
L×L×L = 45234.84
=35.63cm
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