A juice can is in the shape of a cylinder. it has a height of 122 mm and a diameter of 52 mm. What is the longest straw that can fit completely inside the juice can diagonaly? Round the answer to the nearest tenth.
To find the longest straw that can fit completely inside the cylindrical juice can diagonally, we need to consider the diagonal distance that spans from the bottom of the cylinder to the top, passing through the center. This diagonal is a straight line that forms the hypotenuse of a right-angled triangle where the height of the cylinder is one leg, and the diameter of the base is the other leg.
From the information given:
- Height (h) of the cylinder = 122 mm
- Diameter (d) of the cylinder = 52 mm
- Radius (r) of the cylinder = d/2 = 52 mm / 2 = 26 mm
Using the Pythagorean theorem, where the hypotenuse (c) of a right triangle is related to the other two sides (a and b) through the equation c² = a² + b², we can find the length of the longest straw. In this case, the height of the cylinder represents one side (a), and the radius of the base represents the other side (b). The longest straw would be the hypotenuse (c) of this right triangle.
Thus:
c² = a² + b²
c² = h² + r²
c² = (122 mm)² + (26 mm)²
c² = 14884 mm² + 676 mm²
c² = 15560 mm²
Taking the square root of both sides to find the value of c:
c = √15560 mm²
c ≈ 124.74 mm
Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 124.74 mm. Rounding to the nearest tenth, the answer is 124.7 mm.