Answer to Question #137464 in Geometry for Nirvana

Question #137464
A solid cube metal whose edges are each 70cm is melted and recast
into a rectangular solid whose base is 60cm x 80cm.
1. How high is the rectangular solid in cm?
2. What is the volume of the rectangular solid in m3?
3. Determine the diagonal of the rectangular solid in cm
1
Expert's answer
2020-10-08T16:56:25-0400

a) A side of the solid cube metal =70cm, hence its volume is (70)3 =343,000 cm3


The base of the rectangular solid =60××80=4,800cm2


Hence the height of the rectangular solid =343,0004,800\frac{343,000}{4,800}


h=71.4583 cm


b) 1m=100cm

Hence 1m3=1,000,000cm3


Therefore the Volume of the rectangular solid =343,000cm3


Converting to m3;


343,0001,000,000\frac{343,000}{1,000,000}


=0.343m3


c) Diagonal of a rectangular solid =

l2+w2+h2\sqrt{l^{2} +w^{2} +h^{2}}

Where Length, l=80cm

Width, w=60cm

Height,h=71.4583cm


Thus the diagonal =(80)2+(60)2+(71.4583)2=\sqrt{(80)^{2} +(60)^{2} +(71.4583)^{2}}



=(6400)2+(3600)2+(5106.29)2=\sqrt{(6400)^{2} +(3600)^{2} +(5106.29) ^{2}}



=122.90cm

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