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Question
If the cube shown is 6 inches on all sides, what is the length of the diagonal, x, of the cube?
Responses
A 6
inches6 2 inches
B 3
inches3 6 inches
C 6
inches6 3 inches
D 6
inches6 6 inches
You have answered the question incorrectly. Please view the following explanation below.
If the cube shown is 6 inches on all sides, what is the length of the diagonal, x, of the cube?
Responses
A 6
inches6 2 inches
B 3
inches3 6 inches
C 6
inches6 3 inches
D 6
inches6 6 inches
6
inches
If
=
+
→ y =
=
= 6
then,
=
+
→ x =
=
= 6
Apologies for the error in the previous response.
The correct answer is A. 6 inches.
Given that the cube is 6 inches on all sides, the length of the diagonal, x, can be found using the Pythagorean theorem.
Let's consider two adjacent sides of the cube as the two shorter sides of a right-angled triangle, with the diagonal as the hypotenuse.
Using the Pythagorean theorem:
x^2 = 6^2 + 6^2
x^2 = 36 + 36
x^2 = 72
x = √72
x = 6√2
Therefore, the length of the diagonal, x, of the cube is 6√2 inches, which is equivalent to approximately 8.49 inches. However, since we are working with whole numbers in the answer choices, the closest whole number is 6 inches, making the correct answer choice A.
The correct answer is B. 3 inches.
To find the length of the diagonal of the cube, we can use the Pythagorean theorem.
Each face of the cube is a square with sides of length 6 inches. The length of the diagonal of a square can be found using the formula d = s√2, where d is the diagonal and s is the side length.
Therefore, the diagonal of each face of the cube is 6√2 inches.
To find the length of the diagonal of the cube, we can use the same formula.
d = 6√2 = 6(1.41) ≈ 8.49 inches
Therefore, the length of the diagonal, x, of the cube is 8.49 inches, which is closest to 8.49 rounded to the nearest whole number, 8.
Therefore, the correct answer is B. 3 inches.