Help will mark brainlist if it correct If each edge of a cube is increased by 2 inches, the A. volume is increased by 8 cubic inches
B. area of each face is increased by 4 square

C. diagonals of each face is increased by 2 inches
D. sum of these edges is increased by 24 inches

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 + 24

An increase of 24.

D. sum of these edges is increased by 24 inches -- True

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