问题 解答题

一个倒圆锥形容器,它的轴截面是正三角形,在容器内注入水,并放入一个半径为r的铁球,这时水面恰好与球的上面相切,将球从圆锥内取出后,求圆锥内的水深.

答案

如图.在容器内注入水,并放入一个半径为r的铁球,这时水面记为AB,

将球从圆锥内取出后,这时水面记为EF.

三角形PAB为轴截面,是正三角形,

三角形PEF也是正三角形,圆O是正三角形PAB的内切圆.

由题意可知,DO=CO=r,AO=2r=OP,AC=

3
r,

V=

4
3
πr3VPC=
1
3
π(
3
r)
2
?3r=3πr3

又设HP=h,则EH=

3
3
h

V=

1
3
π(
3
3
h)2?h=
π
9
h3

∵V+V=VPC

π
9
h3+
4
3
πr3
=3πr3

h=

315
r

即圆锥内的水深是

315
r.

实验题
阅读理解

For a girl who's interested in fashion, what would be the dream job? Being a model? Probably

no–-that's for a pencil thin who doesn't eat. One answer is, fashion stylist.

Girls can find it hard to ignore this attractiveness and the field is opening up to normal girls,

not only style or fashion design majors(某专业的学生). "It looked too high before, but now I

find it more approachable," said Xue Rui, 22, a Fudan University Chinese literature graduate who works as an assistant stylist at Hermès in Shanghai. "There is no certain principle in dressing up models, and you can try every way with your own distinct taste to make them pretty and attractive." Some professionals said that Xue's not mistaken.

The attractiveness of this work is not only in the wonderful clothes. Now it's a career with a bright future and pay packet. The income can allow you to buy expensive clothes and, with your name and photo appearing on pages, readers will remember your fashion tips.

A stylist at a fashion magazine can have some unique rights. You have a chance to contact famous persons and dress them up in a style you like. You need to cooperate with top photographers and select places around the world to take photos in. You might also be invited to fashion shows of top brands and can select some of the favorite clothes.

"You have to be ‘all-round’:from hair and make up to clothes, shoes, and accessories (配饰) to the event," said He Qing, 21, a junior in fashion design at the Beijing Institute of Fashion Technology. "You have to know everything, and handle several things at the same time. It's challenging. That's why I love it."

So, remember girls, you've been warned.

小题1: The underlined phrase “ pay packet” (paragraph 3)  means________.

A.a large bag

B.a large amount of money

C.chances

D.choices小题2:Which of the following statements is true according to the passage?

A.There are certain principles in dressing up models.

B.The only attractiveness of this work is in the wonderful clothes.

C.Only style or fashion design majors can work as a fashion stylist.

D.A stylist knows how to make a person beautiful, from head to toe。小题3:What is the unique right a stylist at a fashion magazine can have?

A.You have a chance to contact celebrities and dress them up in a style you like.

B.You need to cooperate with top photographers and select places around the world to take photos in.

C.You might also be invited to fashion shows of top brands and can select some of the favorite clothes.

D.All of above小题4: What will the author write in the 6th paragraph?

A.Top brands that fashion stylists like best.

B.Various fashion shows

C.Difficulties that fashion stylists may meet

D.Other dream jobs