As shown in the figure, a chopstick with a length of 24cm is placed in a cylindrical water cup with a diameter of 5cm at the bottom and a height of 12cm. If the length of the chopstick exposed on the outside is HCM, the value range of H is () A. 0＜h≤11B. 11≤h≤12C. h≥12D. 0＜h≤12

As shown in the figure, a chopstick with a length of 24cm is placed in a cylindrical water cup with a diameter of 5cm at the bottom and a height of 12cm. If the length of the chopstick exposed on the outside is HCM, the value range of H is () A. 0＜h≤11B. 11≤h≤12C. h≥12D. 0＜h≤12

When the chopsticks are perpendicular to the bottom of the cup, h is the largest, h is the largest = 24-12 = 12cm. When the chopsticks and the bottom of the cup and the height of the cup form a right triangle, h is the smallest, as shown in the figure: at this time, ab = AC2 + BC2 = 122 + 52 = 13cm, ｜ H = 24-13 = 11cm

A 24 cm long chopstick is placed in a cylindrical cup with a diameter of 5 cm and a height of 12 cm on the bottom?

From Pythagorean theorem
The length in the cup is √ (5 ^ 2 + 12 ^ 2) = 13
24-13=11
So the length of chopsticks exposed is 11cm

As shown in the figure, a chopstick with a length of 15cm is placed in a cylindrical water cup with a bottom diameter of 5cm and filled with water. The known water depth is 12cm. If the length of the chopstick above the water is HCM, then the value range of H is______ ．

∵ put a 15cm long chopstick in a cylindrical water cup with a bottom diameter of 5cm and a height of 12cm, ∵ in the cup, the shortest chopstick is equal to the height of the cup, and the longest is equal to the length of the beveled edge of the cup, ∵ when the shortest chopstick in the cup is equal to the height of the cup, H = 12, and the longest is equal to the length of the beveled edge of the cup, that is, H = 122 + 52 = 13, ∵ the value range of H is: (15-13) ≤ h ≤ (1) So the answer is: 2cm ≤ h ≤ 3cm