Answer:
88 square units.
Step-by-step explanation:
Volume of cuboid = length * width *height
total surface area of the = 2*(LB+BH+HL)
where
L = length
B = width
H = Height
_____________________________
Given
The length, width, and height of a
rectangular solid are in the ratio of
3:2:1
let the
length = 3x
width = 2x
and height = x
Volume of box in terms of x = 3x*2x*x = [tex]6x^3[/tex]
Given that volume if box is 48 cubic units
thus
[tex]6x^3 = 48\\x^3 = 48/6= 8\\x = \sqrt[3]{8} = 2[/tex]
Thus,
length = 3x = 3*2 = 6
width = 2x = 2*2 = 4
and height = x = 2
Now
total surface area of the box = 2(6*4 + 4*2+2*6) = 2(24+8+12)
total surface area of the box = 2*44 = 88
Thus, total surface area of the box is 88 square units.
