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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 18,124

M # 1

A cone, hemisphere and a cylinder have equal bases and same heights. What will be the ratio of their volumes?

**Science without religion Is lame, religion without science is blind - Albert Einstein**.**Knowledge is of two kinds. We know a subject ourselves, or we know where we can find information upon it - Samuel Johnson.**

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**ganesh****Moderator**- Registered: 2005-06-28
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M # 2

The diagonals of a rhombus are 10 cm and 24 cm. What is (i) the perimeter of the rhombus? (ii) area of the rhombus?

**Science without religion Is lame, religion without science is blind - Albert Einstein**.**Knowledge is of two kinds. We know a subject ourselves, or we know where we can find information upon it - Samuel Johnson.**

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**ganesh****Moderator**- Registered: 2005-06-28
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M # 3

What is the length of the longest pole that can be placed inside a room of length 12 m, breadth 4 m and height 3 m?

**Science without religion Is lame, religion without science is blind - Albert Einstein**.**Knowledge is of two kinds. We know a subject ourselves, or we know where we can find information upon it - Samuel Johnson.**

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

m#2 perimeter:4.13=52

area:240

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**krassi_holmz****Real Member**- Registered: 2005-12-02
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m#3:13

m#1:Pir^2h/3, Pir^2h,3Pir^2h/8

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**ganesh****Moderator**- Registered: 2005-06-28
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M # 3 : krassi_holmz, you're correct! The answer is 13 m.

M # 2 : Perimeter = 52 m, correct! Area=?

M # 1 : Try again

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**krassi_holmz****Real Member**- Registered: 2005-12-02
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m#2

area: not 240, 20/2=120!

1# let someone other try

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**ganesh****Moderator**- Registered: 2005-06-28
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**Science without religion Is lame, religion without science is blind - Albert Einstein**.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

thanks

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**mathsyperson****Moderator**- Registered: 2005-06-22
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M # 1 (and here's a *b* to put the post back in the natural key. )

The cone has a volume of 1/3πr²h.

The hemisphere has a volume of 2/3πr³.

The cylinder has a volume of πr²h.

r = h, so the hemisphere's volume can be written as 2/3πr²h.

Taking out all of the common factors gives ratios of 1/3:2/3:1.

Scaling this up makes the ratios 1:2:3.

Why did the vector cross the road?

It wanted to be normal.

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**ganesh****Moderator**- Registered: 2005-06-28
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Well done, mathsyperson

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**ganesh****Moderator**- Registered: 2005-06-28
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M # 4

A spherical iron ball is dropped into a cylindrical

vessel of base diameter 14 cm, containing water. The water

level is increased by 9 1/3 cm. What is the radius of the ball?

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**Patrick****Real Member**- Registered: 2006-02-24
- Posts: 1,005

M#4 -

Determine the volume of the ball:

π7²*9 1/3 = 1436.755cm³

(how do I write pi here?)

And then the radius has to be the square root of:

1436.755/(4/3)*π

which is(about) = 18.52cm

(if this is incorrect, it's because I'm tiiiired )

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**mathsyperson****Moderator**- Registered: 2005-06-22
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I edited your post to include π. To write pi as a symbol, just stick a : in front of it.

You're right about the volume of the sphere, although it would be easier to leave it as 7²*π*9 1/3.

This has to equal 4/3πr³.

The π's cancel out, and you can divide by 4/3 on each side to get 7²*7 = r³.

And that makes the radius of the sphere 7cm.

Why did the vector cross the road?

It wanted to be normal.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 18,124

Well done, Patrick and mathsyperson

**Science without religion Is lame, religion without science is blind - Albert Einstein**.

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**ganesh****Moderator**- Registered: 2005-06-28
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M # 5

How many metres of cloth 11m wide would be required to make a conical tent of base radius 7m and height is 24m?

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**irspow****Member**- Registered: 2005-11-24
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**ganesh****Moderator**- Registered: 2005-06-28
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Well done, irspow!

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**ganesh****Moderator**- Registered: 2005-06-28
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M # 6

A silver cup has the shape of a hemisphere surmounted by a cylinder.The diameter of the sphere is 10.5 cm and the total height of the cup is 11.25 cm. Find its capacity.

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**ganesh****Moderator**- Registered: 2005-06-28
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M # 7

Water flows through a cylindrical pipe of internal radius 3.5 cm at 5m per second. Calculate the volume of water in litres discharged by the pipe in one minute.

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**ganesh****Moderator**- Registered: 2005-06-28
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M # 8

A cylindrical jar of radius 6 cm contains oil. Iron spheres each of radius 1.5 cm are immersed in the oil. How many spheres are necessary to raise the level of the oil by 2 cm?

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**JaneFairfax****Member**- Registered: 2007-02-23
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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 18,124

Answer to M # 8:-

Perfectly correct, Janefairfax!

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ganesh wrote:

M # 1

A cone, hemisphere and a cylinder have equal bases and same heights. What will be the ratio of their volumes?

OMG!

This question came in our Annual Exams last year.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 18,124

Hi,

Interesting, Agnishom!

M # 9. A tailor has 37.5 meters of cloth and he has to make 8 pieces out of a meter of cloth. How many pieces can he make out of this cloth?

**Science without religion Is lame, religion without science is blind - Albert Einstein**.

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