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 inches
D. sum of the edges is increased by 24 inches
try volume
Vnew = (x+2)(x+2)(x+2) big mess
try area
Anew = (x+2)(x+2) = x^2 + 4 x + 4
not this for sure
try that perimeter thing
how many edges?
4bottom +4top +4verticals = 12 edges
12 * 2 = 24 !!! winner
what's c?
I kind of have the same question and my c is that the diagonal of each face is increased by 2 inches. If you need me to disprove that then here you go
Let x represent the side.
Split the square into 2 triangles.
Using the special triangles we know it's a 45, 45, 90 because it's an isosceles triangle. Therefore the diagonal of the triangle before it was added by 2 would be x radical 2.
After you add 2 to all the sides the diagonal would be x+2 multiplied by radical 2 and it's not the same becuase you are technically distributing radical 2 to all the terms so it would be increased by 2 radical 2 instead of being increased by 2 inches
To find the answer, let's first understand the effects of increasing the edge length of a cube on its volume, surface area of each face, and the sum of its edges.
1. Volume:
The volume of a cube is given by the formula V = a³, where 'a' is the length of each edge. Increasing the edge length by 2 inches means the new edge length is (a + 2) inches. So the new volume V' is (a + 2)³.
To calculate the increase in volume, we subtract the original volume from the new volume:
Increase in volume = V' - V = (a + 2)³ - a³.
2. Surface area:
The surface area of a cube is given by the formula A = 6a², where 'a' is the length of each edge. Increasing the edge length by 2 inches means the new edge length is (a + 2) inches. So the new surface area A' is 6(a + 2)².
To calculate the increase in surface area, we subtract the original surface area from the new surface area:
Increase in surface area = A' - A = 6(a + 2)² - 6a².
3. Sum of edges:
The sum of the edges of a cube is given by the formula S = 12a, where 'a' is the length of each edge. Increasing the edge length by 2 inches means the new edge length is (a + 2) inches. So the new sum of edges S' is 12(a + 2).
To calculate the increase in the sum of edges, we subtract the original sum of edges from the new sum of edges:
Increase in sum of edges = S' - S = 12(a + 2) - 12a.
Now that we have found the formulas for each quantity and how to calculate the increases, we can determine which option is correct.
A. Increase in volume = (a + 2)³ - a³
B. Increase in surface area = 6(a + 2)² - 6a²
C. Increase in sum of edges = 12(a + 2) - 12a
By comparing the expressions in each option, we can see that the correct answer is:
D. The sum of the edges is increased by 24 inches because the factor 12 in the expression 12(a + 2) - 12a represents the number of edges, and increasing each edge by 2 inches will cause each of the 12 edges to increase by 2 inches, resulting in a total increase of 24 inches.