What is the measurement of the longest line segment in a right rectangular prism that is 11.2 centimeters long, 6.6 centimeters wide, and 6 centimeters tall?
The longest line segment is ___ cm.
(Round to the nearest tenth as needed.)
What is the measurement of the longest line segment in a right rectangular prism that is 11.2 centimeters long, 6.6 centimeters wide, and 6 centimeters tall?
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To find the longest line segment in a right rectangular prism, we calculate the space diagonal using the formula:
[ d = sqrt{l^2 + w^2 + h^2} ]
where:
– ( l ) = length = 11.2 cm
– ( w ) = width = 6.6 cm
– ( h ) = height = 6 cm
Now, substituting the values:
1. Calculate ( l^2 ):
[ (11.2)^2 = 125.44 ]
2. Calculate ( w^2 ):
[ (6.6)^2 = 43.56 ]
3. Calculate ( h^2 ):
[ (6)^2 = 36 ]
4. Add these values:
[ 125.44 + 43.56 + 36 = 205 ]
5. Now take the square root:
[ d = sqrt{205} approx 14.3 ]
Therefore, the length of the longest line segment (the space diagonal) is approximately 14.3 cm.