Question

pls. help
the volume of a rectangular parallelepiped is 162 cubic units. the three dimensions are in the ratio 1:2:3. find the total surface area

Answer 1

V = (length) (width) (height)
The dimensions are 1:2:3 so:

V = 1 (length) * 2 (width) * 3 (height)
Because the values don't matter and are all relative to one another we can assume they are all base x.

V = 1 (x) * 2 (x) * 3 (x)

Answer 2

Solve for x first, then find the surface area

Answer 3

Twice the surface of the base down= 2(x (2x)) 4 x^2

Answer 4

Lateral Area = perimeter of the base times 3x = ( x+ 2x + x + 2x)(3x)=18x^2
Total area = 4 x^2 + 18 x^2 = 22 x^2

Notice
There is an equal sign missing between 2(x (2x)) and 4 x^2
It should have been
2(x (2x)) =4 x^2

Answer 5

If you know x, you will be done.
162 = x (2x)(3x) =6 x^3
Solve it, you find x=3

Answer 6

Total area
22 x^2 = 22(9) =198