To find the longest straw that can fit completely inside the juice can diagonally, we can use the Pythagorean theorem.
The diagonal of the juice can forms a right triangle with the height and diameter of the can.
We can consider the diameter of the can as the hypotenuse of the right triangle, and the height as one of the legs.
Using the Pythagorean theorem, we can solve for the other leg, which represents the longest straw that can fit diagonally inside the can.
The formula for the Pythagorean theorem is:
a^2 + b^2 = c^2
where a and b are the legs of the right triangle and c is the hypotenuse.
In this case, the diameter is the hypotenuse and the height is one of the legs.
Plugging in the given values:
a^2 + 122^2 = 52^2
a^2 + 14884 = 2704
a^2 = 12344
a = √12344
a ≈ 111.1
Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 111.1 mm. Rounding to the nearest tenth, the longest straw is approximately 111.1 mm. Answer: \boxed{111.1}.
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.
2 answers
An illustration shows a square pyramid with labeled parts. The left, front and right faces of the pyramid and base are visible. The back face is not visible. The back base edge is not visible but its position is indicated by a dashed line. The front base edge shows a length of 40 feet. A dotted line extends from the interior of the vertex straight down to the center of the base and is labeled h. A right angle is indicated where the dotted height line meets the base. Another dotted line extends from the center of the base where the height line meets to the center of the right base edge. A dotted line extends from the right base edge straight up the center of the right face of the prism and meets the height line at the vertex. This dotted line shows a slant height of 25 feet. Apply the Pythagorean Theorem to determine the height of the square pyramid, h . Round the answer to the nearest tenth. (1 point) Responses 47.2 ft. 47.2 ft. 15.0 ft. 15.0 ft. 31.2 ft. 31.2 ft. 32.0 ft. 32.0 ft.