SOLUTION: 1.The length,width,and height of a rectangular solid are in the ratio of 3:2:1.If the volume of the box is 48,what is the total surface area of the box? (A)27 (B)32 (C)44 (D)64

Question 476073: 1.The length,width,and height of a rectangular solid are in the ratio of 3:2:1.If the volume of the box is 48,what is the total surface area of the box?
(A)27
(B)32
(C)44
(D)64
(E)88
2.A cube whose volume is 1/8 cubic foot is placed on top of a cube whose volume is 1 cubic foot.The two cubes are then placed on top of a third cube,whose volume is 8 cubic feet.What is the height,in inches,of the stacked cubes?
(A)30
(B)40
(C)42
(D)44
(E)64
Please help me with these problems.Thank you so much for giving your time to help me with these problems.I really appreciate it.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1.The length,width,and height of a rectangular solid are in the ratio of 3:2:1.
If the volume of the box is 48,what is the total surface area of the box?
:
let x = "the multiplier"
The three dimensions, then are; 3x by 2x by x
then the volume
3x * 2x * x = 48
6x^3 = 48
Divide both sides by 6
x^3 = 48/6
x^3 = 8
x = the cube root of 8 which is:
x = 2 the multiplier
Then the Dimensions are 6 by 4 by 2
:
find the surface area:
S.A. = 2(L*W) + 2(L*H) + 2(W*H)
S.A. = 2(6*4) + 2(6*2) + 2(4*2)
S.A. = 48 + 24 + 16
S.A. = 88 sq units
:
:
2.A cube whose volume is 1/8 cubic foot is placed on top of a cube whose volume is 1 cubic foot.
The two cubes are then placed on top of a third cube,whose volume is 8 cubic feet.
;
Find the length of the side of each cube, (the side is the cube root of the vol)
= ft
:
= 1 ft
:
= 2 ft
What is the height,in inches, of the stacked cubes?
h = + 1 + 2 = 3 ft which is: 3(12) + 6 = 42 inches high

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