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A juice can is in the shape of a cylinder. It has a height of 122 mm in a diameter of 52 mm what is the longest straw that can...Asked by Alto Saxophone
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. :)
Answers
Answered by
Alto Saxophone
thats not right
Answered by
Alto Saxophone
132.6
Answered by
GPT-4o mini
To find the length of the longest straw that can fit diagonally inside the cylindrical juice can, we can visualize the problem as finding the length of a diagonal inside a cylinder. The longest diagonal will stretch from one point on the base of the cylinder to the opposite point on the top face.
The diagonal, \(d\), inside a cylinder can be calculated using the formula derived from the Pythagorean theorem for a right triangle formed by the height of the cylinder and the diameter of the cylinder's base:
\[
d = \sqrt{h^2 + r^2}
\]
where:
- \(h\) is the height of the cylinder,
- \(r\) is the radius of the cylinder.
First, we need to find the radius of the base. Given the diameter is \(52\) mm, the radius \(r\) is:
\[
r = \frac{\text{diameter}}{2} = \frac{52 \, \text{mm}}{2} = 26 \, \text{mm}
\]
Now we can substitute the values into the formula. The height \(h\) is given as \(122\) mm.
Now we compute the diagonal \(d\):
\[
d = \sqrt{h^2 + r^2} = \sqrt{122^2 + 26^2}
\]
Calculating each squared term:
\[
122^2 = 14884 \quad \text{and} \quad 26^2 = 676
\]
Adding these values together:
\[
14884 + 676 = 15560
\]
Now, taking the square root to find \(d\):
\[
d = \sqrt{15560} \approx 124.0 \, \text{mm}
\]
Thus, the length of the longest straw that can fit completely inside the juice can diagonally is approximately:
\[
\boxed{124.0} \, \text{mm}
\]
The diagonal, \(d\), inside a cylinder can be calculated using the formula derived from the Pythagorean theorem for a right triangle formed by the height of the cylinder and the diameter of the cylinder's base:
\[
d = \sqrt{h^2 + r^2}
\]
where:
- \(h\) is the height of the cylinder,
- \(r\) is the radius of the cylinder.
First, we need to find the radius of the base. Given the diameter is \(52\) mm, the radius \(r\) is:
\[
r = \frac{\text{diameter}}{2} = \frac{52 \, \text{mm}}{2} = 26 \, \text{mm}
\]
Now we can substitute the values into the formula. The height \(h\) is given as \(122\) mm.
Now we compute the diagonal \(d\):
\[
d = \sqrt{h^2 + r^2} = \sqrt{122^2 + 26^2}
\]
Calculating each squared term:
\[
122^2 = 14884 \quad \text{and} \quad 26^2 = 676
\]
Adding these values together:
\[
14884 + 676 = 15560
\]
Now, taking the square root to find \(d\):
\[
d = \sqrt{15560} \approx 124.0 \, \text{mm}
\]
Thus, the length of the longest straw that can fit completely inside the juice can diagonally is approximately:
\[
\boxed{124.0} \, \text{mm}
\]
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