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## #1 2006-02-26 20:20:55

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

### Mensuration

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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## #2 2006-02-26 22:40:08

ganesh
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Posts: 18,124

### Re: Mensuration

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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## #3 2006-02-27 00:02:51

ganesh
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Posts: 18,124

### Re: Mensuration

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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## #4 2006-02-27 00:15:14

krassi_holmz
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Registered: 2005-12-02
Posts: 1,905

### Re: Mensuration

m#2 perimeter:4.13=52
area:240

IPBLE:  Increasing Performance By Lowering Expectations.

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## #5 2006-02-27 00:21:19

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

### Re: Mensuration

m#3:13
m#1:Pir^2h/3, Pir^2h,3Pir^2h/8

IPBLE:  Increasing Performance By Lowering Expectations.

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## #6 2006-02-27 02:05:06

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

### Re: Mensuration

M # 3 : krassi_holmz, you're correct! The answer is 13 m.
M # 2 : Perimeter = 52 m, correct! Area=?
M # 1 : Try again

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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## #7 2006-02-27 02:34:22

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

### Re: Mensuration

m#2
area: not 240, 20/2=120!
1# let someone other try

IPBLE:  Increasing Performance By Lowering Expectations.

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## #8 2006-02-27 02:47:23

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

### Re: Mensuration

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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## #9 2006-02-27 03:13:32

krassi_holmz
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Registered: 2005-12-02
Posts: 1,905

### Re: Mensuration

thanks

IPBLE:  Increasing Performance By Lowering Expectations.

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## #10 2006-02-27 06:35:50

mathsyperson
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Registered: 2005-06-22
Posts: 4,900

### Re: Mensuration

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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## #11 2006-02-27 16:42:15

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

### Re: Mensuration

Well done, mathsyperson

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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## #12 2006-02-28 01:08:45

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

### Re: Mensuration

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?

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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## #13 2006-02-28 11:30:56

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

### Re: Mensuration

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

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

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## #14 2006-02-28 12:22:15

mathsyperson
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Registered: 2005-06-22
Posts: 4,900

### Re: Mensuration

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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## #15 2006-02-28 16:12:58

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

### Re: Mensuration

Well done, Patrick and mathsyperson

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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## #16 2006-03-01 03:49:17

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

### Re: Mensuration

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?

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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## #17 2006-03-01 13:09:04

irspow
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Registered: 2005-11-24
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## #18 2006-03-01 15:56:08

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

### Re: Mensuration

Well done, irspow!

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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## #19 2006-03-02 17:41:14

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

### Re: Mensuration

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.

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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## #20 2006-03-05 17:17:01

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

### Re: Mensuration

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.

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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## #21 2006-03-08 16:12:27

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

### Re: Mensuration

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?

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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## #22 2009-01-04 09:20:33

JaneFairfax
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## #23 2009-01-04 16:34:00

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

### Re: Mensuration

Perfectly correct, Janefairfax!

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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## #24 2013-09-13 22:28:23

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 22,207
Website

### Re: Mensuration

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.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
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## #25 2014-05-31 17:00:13

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

### Re: Mensuration

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.
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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