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**ganesh****Moderator**- Registered: 2005-06-28
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M # 1

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

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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?

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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?

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**krassi_holmz****Real Member**- Registered: 2005-12-02
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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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Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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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
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Well done, Patrick and mathsyperson

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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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!

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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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.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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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: 21,484

Answer to M # 8:-

Perfectly correct, Janefairfax!

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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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
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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?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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