A box shaped like a right rectangular prism measures 5 centimeters by 3 centimeters by 2 centimeters. What is the length of the interior diagonal of the prism to the nearest hundredth?
A) 6.16
B) 6.32
C) 7.07
D) 7.28
Length of the interior diagonal of the right rectangular prism.
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To find the length of the interior diagonal of a right rectangular prism, you can use the formula:
[ d = sqrt{l^2 + w^2 + h^2} ]
where ( l ) is the length, ( w ) is the width, and ( h ) is the height of the prism. In this case:
– ( l = 5 ) cm
– ( w = 3 ) cm
– ( h = 2 ) cm
Now, we can calculate the diagonal:
1. Square each dimension:
– ( l^2 = 5^2 = 25 )
– ( w^2 = 3^2 = 9 )
– ( h^2 = 2^2 = 4 )
2. Add these values together:
– ( 25 + 9 + 4 = 38 )
3. Take the square root of the sum:
– ( d = sqrt{38} approx 6.16 )
So, the length of the interior diagonal of the prism is approximately ( 6.16 ) cm, which corresponds to option A.
Answer: A) 6.16