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

ganesh
Registered: 2005-06-28
Posts: 28,456

### Mensuration

M # 1

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

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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

ganesh
Registered: 2005-06-28
Posts: 28,456

### 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?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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

ganesh
Registered: 2005-06-28
Posts: 28,456

### 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?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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

krassi_holmz
Real Member
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
Registered: 2005-06-28
Posts: 28,456

### 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

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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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
Registered: 2005-06-28
Posts: 28,456

### Re: Mensuration

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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

krassi_holmz
Real Member
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
Moderator
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
Registered: 2005-06-28
Posts: 28,456

### Re: Mensuration

Well done, mathsyperson

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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

ganesh
Registered: 2005-06-28
Posts: 28,456

### 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?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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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
Moderator
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
Registered: 2005-06-28
Posts: 28,456

### Re: Mensuration

Well done, Patrick and mathsyperson

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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

ganesh
Registered: 2005-06-28
Posts: 28,456

### 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?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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

irspow
Member
Registered: 2005-11-24
Posts: 457

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## #18 2006-03-01 15:56:08

ganesh
Registered: 2005-06-28
Posts: 28,456

### Re: Mensuration

Well done, irspow!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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

ganesh
Registered: 2005-06-28
Posts: 28,456

### 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.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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

ganesh
Registered: 2005-06-28
Posts: 28,456

### 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.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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

ganesh
Registered: 2005-06-28
Posts: 28,456

### 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?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

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

ganesh
Registered: 2005-06-28
Posts: 28,456

### Re: Mensuration

Perfectly correct, Janefairfax!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,861
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.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #25 2014-05-31 17:00:13

ganesh
Registered: 2005-06-28
Posts: 28,456

### 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?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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