Question
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
Ask by Barker Cummings. in the United States
Mar 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The longest straw that can fit diagonally inside the juice can is approximately 124.7 mm.
Solution
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.
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Mind Expander
To find the longest straw that can fit diagonally inside the juice can, we can use the Pythagorean theorem. First, calculate the radius of the base of the cylinder, which is half of the diameter: 52 mm / 2 = 26 mm. Then, use the formula for the diagonal length \(d\) of the cylinder, given by \(d = \sqrt{h^2 + (2r)^2}\). Plugging in the values, we have \(d = \sqrt{122^2 + (52)^2}\). This gives \(d = \sqrt{14884 + 2704} = \sqrt{17588} \approx 132.6\) mm. So, the longest straw that can fit completely inside the juice can diagonally is approximately **132.6 mm**.