Question 776778: Dear Math Tutor,
Two cubes are places next to each other. the length of each of the edges of the larger cube is 4cm. if the ratio of their surface areas is 1:4 calculate: a)the surface area of the small cube. b) the length of the an edge of the small cube
the ratio part is confusing me. how do i use the ratio to find a)?
thank you.
Best wishes,
Nats
Found 4 solutions by stanbon, Cromlix, htmentor, rothauserc:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Two cubes are placed next to each other. the length of each of the edges of the larger cube is 4cm.
The surface area of each side of that cube is 16 cm^2
The total surface area of that cube is 6*16 = 96 cm^2
==========================================================
if the ratio of their surface areas is 1:4 calculate:
----------------
a)the surface area of the small cube = (1/4) the surface
area of the larger cube = (1/4)96 = 26 cm^2
-----------------------
b) the length of the an edge of the small cube
So each face of the smaller cube has area = (1/6)26 = 13/3
Therefore each edge of the smaller cube is sqrt(13/3) = (13/3)sqrt(3)
================
Cheers,
Stan H.
================
Answer by Cromlix(4381)  (Show Source):
You can put this solution on YOUR website! Surface Area of large cube:
Six times (number of faces)
times area of 1 face.
6 * 4 * 4 = 96 cm^2
If the ratio of small to large is 1:4
96/4 = 24 cm^2
6 sides of small cube = 24 cm^2
1 side of small cube = 4 cm^2
Square root of 4 = 2cm
The size of a side of the small
cube = 2cm.
Hope this helps.
:-)
Answer by htmentor(1343)  (Show Source):
You can put this solution on YOUR website! If a cube has side length s then the surface area = 6s^2
For the larger cube s=4, so A = 6*4^2 = 96 cm^2
(a) If the areas are in the ratio 1:4, then the smaller cube has surface area 96/4 = 24 cm^2
(b) Therefore, the small cube has edge length l = sqrt(24/6) = 2 cm
Answer by rothauserc(4718)  (Show Source):
You can put this solution on YOUR website! Surface area of a cube = 6*x^2
Surface area of the larger cube is 6*4^2 = 96 cm^2
now the ratio of the smaller cube's surface area to the larger cube's surface area is 1/4, we can write
1/4 = surface area of smaller cube / 96
cross multiply the two fractions and we ge
surface area of smaller cube * 4 = 96
a)surface area of smaller cube = 24 cm^2
b)24 = 6*n^2
4 = n^2
n = 2 cm
|
|
|
