问题 选择题

将一个10cm×10cm×10cm的立方体切为1cm×1cm×1cm的小立方体.用这些小立方体重新黏合成一个内部允许有空洞但表面无空洞的大立方体.这个空心的立方体要尽可能的大,请问最多能剩下多少个小立方体没有用到?(  )

A.32

B.81

C.125

D.134

答案

∵将一个10cm×10cm×10cm的立方体切为1cm×1cm×1cm的小立方体.

∴原来有1000个小立方体,

现在粘的最大空间利用的就是里面全是空的,只外面一层有.

假设新的立方体边长为X个小立方体,那么现在计算总的立方体数:

6个面中间:(x-2)(x-2),

12条棱中间:各(x-2)个,

8个顶角各一个,

加起来就是(x-2)(x-2)×6+(x-2)×12+8=6(x-1)2+2≤1000,

现在就要找到使上面那个式子小于等于1000的最小的x,

试下来是13,

此时上面试子的结果是866,

也就是剩下的小立方体的个数是1000-866=134.

故选:D.

阅读理解

E

Computer mouse is no longer so strong. A Canadian engineer has invented a system that enables a computer user to push a cursor(光标)across a screen simply by moving his or her nose .He calls his nose-driven mouse a mouse.

The inventor ,Dmity Gorodnichy ,came up with the idea for the mouse while building computer software that would help astronauts operate the Canadarm—a long robotic arm on the U.S. space shuttle .His system employs a web-camera that recognizes a computer user’s nose from 25 pixels ,or points of light. Dmity chose the nose because its position remains relatively constant no matter which way the head moves .The system keeps track of the pixels, and the user matches the movements of his or her nose with the progress of the cursor across the screen.

The mouse keeps track of the eyes too. Two blinks(眨眼)are a “double click,” which turns the mouse on or off.

The mouse has received mixed comments from those who hold opposite opinions. One called it “a pointless waste of technology” . Another predicted that the nouse will fail to catch on because it makes users “look silly.” Dmity has already adapted the nouse for NousePong, a video game ,and NousePaint ,a drawing program.

He also predicts that the mouse will attract the people who have suffered from specific disease-pain ,senselessness ,or trembling in the hand caused by the frequent repetition of movements of the wrist and fingers ,such as typing at a computer keyboard .His next plan is to adapt the nouse for use by paralyzed(瘫痪)patients in hospitals .With two blinks of the eyes ,patients could double-click for help.

72.The best title for this passage is probably      .

A.Mouse Driven by Nose

B.Cursor Moved Without fingers

C.New Computer System for Astronauts

D.New Type of Mouse for Patients

73.The nouse is a system working by means of          .

A.keeping track of the points of light

B.moving one’s nose or blinking

C.moving cursor across the screen

D.matching the user’s nose with eyes

74.The underlined phrase “catch on” means “       ”.

A.become popular     B.be used      C.get improved        D.be made

75.Dmity predicts that the nouse will be more used to help          .

A.those who have eye trouble

B.develop a video game and drawing program

C.those traveling in space

D.the disabled with the hand and paralyzed patients

单项选择题 配伍题