问题 填空题

已知正四棱锥的底面面积为4cm2,体积为4cm3,设它的侧面上的斜高与底面所成角的大小为θ,则sinθ的值是______.

答案

如图,

底面面积为4cm2,底面边长CD=2,.体积为4cm3,高PO=3,

E为CD中点,由正棱锥性质,斜高PE⊥CD,,OE⊥CD,∠PEO为斜高与底面所成角,∠PEO=θ.

在直角三角形POE中,sinθ=

PO
PE
=
3
32+12
=
3
10
10

故答案为:

3
10
10

填空题
阅读理解

It’s generally believed that people act the way they do because of their personalities and attitudes. They recycle their garbage because they care about the environment. They pay $5 for a caramel brulee latte because they like expensive coffee drinks.

It’s undeniable that behavior comes from our inner dispositions(性情), but in many instances we also draw inferences about who we are, as suggested by the social psychologist Daryl Bern, by observing our own behavior. We can be strangers to ourselves. If we knew our own minds, why should we need to guess what our preferences are from our behavior? If our minds were an open book, we would know exactly how much we care about the environment or like lattes. Actually, we often need to look to our behavior to figure out who we are.

Moreover, we don’t just use our behavior to learn about our particular types of character --- we infer characters that weren’t there before. Our behavior is often shaped by little pressures around us, which we fail to recognize. Maybe we recycle because our wives and neighbors would disapprove if we didn’t. Maybe we buy lattes in order to impress the people around us. We should not mistakenly believe that we always behave as a result of some inner disposition.

Whatever pressures there can be or inferences one can make, people become what they do, though it may not be in compliance(符合)with their true desires. Therefore, we should all bear in mind Kurt Vonnegut’s advice: “We are what we pretend to be, so we must be careful about what we pretend to be.”

小题1:According to the passage, personalities and attitudes are commonly believed to _______.

A.determine one’s behavior

B.reflect one’s taste

C.influence one’s surroundings

D.result from one’s habits小题2:Which of the following would Daryl Bern most probably agree with?

A.The return of a wallet can indicate one’s honesty.

B.A kind person will offer his seat to the old.

C.One recycles plastics to protect the environment.

D.One buys latte out of love of coffee.小题3:What can be inferred from the underlined sentence in the passage?

A.We fail to realize our inner dispositions.

B.We can be influenced by outside pressures.

C.Our behavior is the result of our true desires.

D.Our characters can shape our social relationships.小题4:What does the author mainly discusses in the passage?

A.Personalities and attitudes.

B.Preferences and habits.

C.Behavior and personalities.

D.Attitudes and preferences.