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

ganesh
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Registered: 2005-06-28
Posts: 20,102

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

Re: Mensuration

m#2 perimeter:4.13=52
area:240


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

krassi_holmz
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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: 20,102

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 smile


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
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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: 20,102

Re: Mensuration

good.gif


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
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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. smile)

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: 20,102

Re: Mensuration

Well done, mathsyperson up


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
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Registered: 2005-06-28
Posts: 20,102

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

which is(about) = 18.52cm

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


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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: 20,102

Re: Mensuration

Well done, Patrick and mathsyperson smile


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
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Registered: 2005-06-28
Posts: 20,102

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

Re: Mensuration

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

ganesh
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Registered: 2005-06-28
Posts: 20,102

Re: Mensuration

Well done, irspow! smile


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
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Registered: 2005-06-28
Posts: 20,102

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
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Registered: 2005-06-28
Posts: 20,102

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
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Registered: 2005-06-28
Posts: 20,102

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

Re: Mensuration

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

ganesh
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Registered: 2005-06-28
Posts: 20,102

Re: Mensuration

Answer to M # 8:-
Perfectly correct, Janefairfax!
grwrk1.gif


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
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 23,201
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
Moderator
Registered: 2005-06-28
Posts: 20,102

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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