A box in the shape of a rectangular prism has the dimensions shown. To the nearest tenth of a centimeter, how many centimeters long is the interior diagonal of the box?
A rectangular prism with a base that measures 6 centimeters by 8 centimeters, and a height of 11 centimeters. A dashed diagonal line is drawn from one vertex of the base to the opposite vertex of the same base. Another dashed diagonal line is drawn from one vertex of the base to the opposite vertex of the other base.
To find the interior diagonal of the box, we can use the Pythagorean theorem.
Let's label the dimensions of the rectangular prism as follows:
- Length (l) = 8 cm
- Width (w) = 6 cm
- Height (h) = 11 cm
First, we need to find the length of the diagonal of the base of the rectangular prism:
Diagonal of base = √(l^2 + w^2)
Diagonal of base = √(8^2 + 6^2)
Diagonal of base = √(64 + 36)
Diagonal of base = √100
Diagonal of base = 10 cm
Next, we need to find the diagonal of the rectangular prism, using the height (h) as the third side of a right triangle:
Diagonal of box = √(Diagonal of base^2 + h^2)
Diagonal of box = √(10^2 + 11^2)
Diagonal of box = √(100 + 121)
Diagonal of box = √221
Diagonal of box ≈ 14.9 cm
Therefore, the interior diagonal of the box is approximately 14.9 cm.