What is the length of the diagonal for the given rectangular prism to the nearest whole unit?
A rectangular prism is shown. A bold yellow line extends from the upper rear vertex to the lower front right vertex. To the right of the prism the text 'Length equals 8 centimeters', 'Width equals 3 centimeters', and 'Height equals 7 centimeters' is displayed.
A. 10 cm
B. 11 cm
C. 6 cm
D. 13 cm
Using the Pythagorean theorem, the length of the diagonal can be found:
diagonal = sqrt(8^2 + 3^2 + 7^2)
diagonal = sqrt(94)
diagonal ≈ 9.7
Rounding to the nearest whole unit, the length of the diagonal is 10 cm.
Answer: A. 10 cm
To find the length of the diagonal of the rectangular prism, we can use the Pythagorean theorem.
The Pythagorean theorem states that the square of the diagonal is equal to the sum of the squares of the lengths of the three sides. Therefore, we need to find the square root of the sum of the squares of the length, width, and height.
Given that the length is 8 cm, the width is 3 cm, and the height is 7 cm, we can calculate the diagonal as follows:
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 122, we find:
Diagonal ≈ 11.04 cm
To the nearest whole unit, the length of the diagonal is approximately 11 cm.
Therefore, the answer is B. 11 cm.