Question

A solid cuboid has a volume of 40cm^3

The cuboid has a total surface area of 100cm^2
One edge of the cuboid has length 2cm

Find the length of a diagonal of the cuboid
To 3sf

Answer 1

A cuboid is a box-shaped object. It has six sides and all are perpendicular

Formula for volume is:
V=a*b*c
Formula for a surface area is:
A=2*(ab+bc+ac)

We start writting down given information:
V=40cm^3
A=100cm^2
a=2cm

Now we insert this information into formulas:
40=2*b*c
100=2*(2b+bc+2c)

Now we divide both equations by 2:
20=bc
50=2b+bc+2c

We solve first equation for b and insert it into second equation:
b=20/c
50=2*20/c+20/c*c+2c

Now we solve for c:
50=40/c+20+2c
30=40/c+2c
30c-40-2c^2=0
2c^2-30c+40=0
c^2-15c+20=0
c1=13,52
c2=1,48

We got two solutions for c so we will get two solutions for b:
b1=1,48
b2=13,52

Now we know:
a=2cm
b=1,48cm
c=13,52cm

Formula for a diagonal is:

`D= \sqrt{ a^(2) + b^(2) + c^(2) } \\ \\ D= \sqrt{ 2^(2) + 1,48^(2) + 13,52^(2) } \\ \\ D=13,74cm`