15. What is the length of the diagonal for the given rectangular prism to the nearest whole unit? (1 point)
Length = 8 cm
Width=3 cm
Height = 7 cm
O 10 cm
O 11 cm
O 6 cm
O 13 cm
To find the length of the diagonal of the rectangular prism, we can use the Pythagorean theorem, which states that the square of the length of the diagonal is equal to the sum of the squares of the length, width, and height of the rectangular prism.
So,
Diagonal^2 = Length^2 + Width^2 + Height^2
Diagonal^2 = 8^2 + 3^2 + 7^2
Diagonal^2 = 64 + 9 + 49
Diagonal^2 = 122
Taking the square root of both sides, we get:
Diagonal = sqrt(122) ≈ 11
Therefore, the length of the diagonal to the nearest whole unit is 11 cm.
The answer is O 11 cm.
To find the length of the diagonal of a rectangular prism, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the other two sides.
In this case, the length, width, and height of the rectangular prism are given as 8 cm, 3 cm, and 7 cm, respectively.
To find the diagonal, we need to create a right triangle by connecting the diagonal with two sides of the rectangular prism. Let's choose the length and width sides.
Using the Pythagorean Theorem:
Diagonal^2 = Length^2 + Width^2
Substituting in the given values:
Diagonal^2 = 8^2 + 3^2
Diagonal^2 = 64 + 9
Diagonal^2 = 73
To find the length of the diagonal, we need to find the square root of 73:
√73 ≈ 8.544
Rounding to the nearest whole unit, the length of the diagonal is 9 cm.
So, the correct answer is O 9 cm.
To find the length of the diagonal of a rectangular prism, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the diagonal of the rectangular prism represents the hypotenuse of a right triangle, while the length and width of the prism represent the other two sides.
Using the given dimensions:
Length = 8 cm
Width = 3 cm
Height = 7 cm
Let's find the length of the diagonal step-by-step:
Step 1: Calculate the square of the length:
Length Square = 8^2 = 64
Step 2: Calculate the square of the width:
Width Square = 3^2 = 9
Step 3: Calculate the square of the height:
Height Square = 7^2 = 49
Step 4: Add the squares of the three sides together:
64 + 9 + 49 = 122
Step 5: Calculate the square root of the sum:
Diagonal = √122
Rounded to the nearest whole unit, the length of the diagonal is approximately 11 cm.
Therefore, the answer is 11 cm (O 11 cm).