The length of a rectangular solid is twice the width, and the height is three times the width. If the volume?

Question

The length of a rectangular solid is twice the width, and the height is three times the width. If the volume is 162 cubic meters, find the surface area of the solid. Show all work.

Answer 1

[09]
Let the width of the solid be w meter
Therefore by the problem
w*2w*3w=162
6w^3=162
w^3=27
w=3
Therefore the width is 3 meter,length is 6 meter,and height is 9 meter
Total surface area
=2(length*width+width*height+length* height)
=2(6*3+3*9+6*9)
=2(18+27+54)
=2*99=198 sq meter

Answer 2

Assume width = 1 then volume = 6,
so,
width = 27 because volume = 162,
because 162/6 = 27.
length = 2* width = 54 & height = 3 * width = 81.
We know that there are 6 faces & we know the side lengths
so we may work out the surface areas of the 6 faces
& add them together giving us the answer.

Answer 3

Length = 2 * Width
Height = 3 * Width
Volume = Length * Width * Height
162 = (2 * Width) * Width * (3 * Width)
or 162 = 6 * Width^3
or Width^3 = 162/6
or Width^3 = 27
or Width^3 = 3^3
or Width = 3 m
Thererfore, Length = 2 * Width = 6m
and Height = 3 * width = 9m

Surface Area = 2(Length * Width + Length * Height + Width * Height)

No plug in the values in the above equation and you have your answers

Answer 4

L=lenth W=width H=height V=volume
SA=surface area

L=2W
H=3W

therfore
V=WLH
=W(2W)(3W)
=6W^3
=162 m^3
W^3=27
W=3 m
L=6 m
H=9 m

SA=2(WL+WH+LH)
=2(18+27+54)
=198 m^2

Answer 5

so let w = width
l = length = 2w
h = height = 3w
so volume = wlh = w*2w*3w = 6w^3 = 162
w = 3
surface area =
2lh + 2lw + 2hw = 2(2w*3w) = 2(2w*w) + 2(3w*w)
= 12w^2 + 4w^2 + 6w^2 = 22w^2 = 22(9) = 198