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 diagonally? Round the answer to the nearest tenth. (1 point) Check answer Remaining Attempts : 3

To find the longest straw that can fit completely inside the juice can diagonally, we need to calculate the diagonal of the cylinder. Given: - Height of the cylinder (h) = 122 mm - Diameter of the cylinder (d) = 52 mm The diagonal of a cylinder can be calculated using the formula: \[ \text{Diagonal} = \sqrt{h^2 + \left(\frac{d}{2}\right)^2} \] Substitute the given values into the formula: \[ \text{Diagonal} = \sqrt{122^2 + \left(\frac{52}{2}\right)^2} \] Now, we can calculate the diagonal of the cylinder. Calculate the value by following steps: - step0: Calculate: \(\sqrt{122^{2}+\left(\frac{52}{2}\right)^{2}}\) - step1: Divide the terms: \(\sqrt{122^{2}+26^{2}}\) - step2: Add the numbers: \(\sqrt{15560}\) - step3: Write as a product: \(\sqrt{4\times 3890}\) - step4: Write in exponential form: \(\sqrt{2^{2}\times 3890}\) - step5: Use the properties of radicals: \(\sqrt{2^{2}}\times \sqrt{3890}\) - step6: Simplify the root: \(2\sqrt{3890}\) The longest straw that can fit completely inside the juice can diagonally is approximately 124.7 mm. Rounded to the nearest tenth, the answer is 124.7 mm.