Answer:
D. sum of these edges is increased by 24 inches -- True
Step-by-step explanation:
Given a cube and its edge is increased by 2 inches.
To study the effect of this increase in the Volume, area of each face, diagonal and sum of edges.
Solution:
Let the side of original cube = a inches.
Formula for volume of cube:
If the side is increased by 2 inches, the side becomes (a+2) inches.
So, new volume,
Using the formula:
So,
Volume increased by 8+6a(a+2) [which is not equal to 8]
So, statement is false:
A. volume is increased by 8 cubic inches -- False
Each face in a cube is a square.
Area of each face, A =
New area, A' =
Using the formula:
Area increased by 4+4a [which is not equal to 4 sq inches]
B. area of each face is increased by 4 square inches -- False
Diagonal of each face =
Increase of 2 in the edge:
New diagonal =
So, increase of not 2.
C. diagonals of each face is increased by 2 inches -- False
There are 12 number of edges in a square.
So sum of all 12 edges = 12a
When edge is increased by 2, sum of all edges = 12(a+2) = 12a + <em>24</em>
An increase of 24.
D. sum of these edges is increased by 24 inches -- True