Answer to Question #137464 in Geometry for Nirvana

Question

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

Answer 1

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 =$\frac{343,000}{4,800}$

h=71.4583 cm

b) 1m=100cm

Hence 1m³=1,000,000cm³

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

Converting to m^3;

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

=0.343m³

c) Diagonal of a rectangular solid =

$$\sqrt{l^{2} +w^{2} +h^{2}}$$

Where Length, l=80cm

Width, w=60cm

Height,h=71.4583cm

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

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

=122.90cm