A mechanical draftsperson needs to find the distance across the corners of a hex-bolt. See the illustration. If the distance across the flats is 3.96 cm, find the distance x across the corners. Round your answer to the appropriate number of significant digits.
A) 7.52 cm
B) 6.32 cm
C) 9.92 cm
D) 7.92 cm
E) 5.22 cm

Question

A mechanical draftsperson needs to find the distance across the corners of a hex-bolt. See the illustration. If the distance across the flats is 3.96 cm, find the distance x across the corners. Round your answer to the appropriate number of significant digits. 
A) 7.52 cm 
B) 6.32 cm 
C) 9.92 cm 
D) 7.92 cm 
E) 5.22 cm

Quizplus · Accepted Answer

The distance across the corners of a hexagonal shape is equal to the diameter of the circle inscribed within the hexagon. Using the given distance across the flats (3.96 cm), we can find the radius of the inscribed circle by dividing the distance across the flats by 2 and then multiplying by the square root of 3. So, radius = (3.96/2) x sqrt(3) = 1.83 cm (rounded to two decimal places). The distance across the corners (x) is simply twice the radius, so x = 2 x 1.83 = 3.66 cm. Rounded to the appropriate number of significant digits, the answer is 3.7 cm, which corresponds to choice D.

A Mechanical Draftsperson Needs to Find the Distance Across the Corners