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

ganesh
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Registered: 2005-06-28
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Mensuration

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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#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?


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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?


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

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

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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Posts: 1,908

Re: Mensuration

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


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

ganesh
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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


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

krassi_holmz
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Re: Mensuration

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


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

ganesh
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Re: Mensuration

good.gif


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

krassi_holmz
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Re: Mensuration

thanks


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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.


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

ganesh
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Re: Mensuration

Well done, mathsyperson up


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

ganesh
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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?


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

Patrick
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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
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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.


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

ganesh
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Re: Mensuration

Well done, Patrick and mathsyperson smile


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

ganesh
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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?


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

irspow
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Registered: 2005-11-24
Posts: 455

Re: Mensuration

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

ganesh
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Re: Mensuration

Well done, irspow! smile


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

ganesh
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Registered: 2005-06-28
Posts: 15,142

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.


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

ganesh
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Registered: 2005-06-28
Posts: 15,142

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.


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

ganesh
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Registered: 2005-06-28
Posts: 15,142

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?


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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: 15,142

Re: Mensuration

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


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

Agnishom
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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.


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

ganesh
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Registered: 2005-06-28
Posts: 15,142

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?


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