Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 12,919

M # 1

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

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 12,919

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?

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 12,919

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?

Character is who you are when no one is looking.

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

m#2 perimeter:4.13=52

area:240

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

m#3:13

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

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 12,919

M # 3 : krassi_holmz, you're correct! The answer is 13 m.

M # 2 : Perimeter = 52 m, correct! Area=?

M # 1 : Try again

Character is who you are when no one is looking.

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

m#2

area: not 240, 20/2=120!

1# let someone other try

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 12,919

Character is who you are when no one is looking.

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

thanks

IPBLE: Increasing Performance By Lowering Expectations.

Offline

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

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.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 12,919

Well done, mathsyperson

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 12,919

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?

Character is who you are when no one is looking.

Offline

**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 )

Support MathsIsFun.com by clicking on the banners.

What music do I listen to? Clicky click

Offline

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

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.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 12,919

Well done, Patrick and mathsyperson

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 12,919

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?

Character is who you are when no one is looking.

Offline

**irspow****Member**- Registered: 2005-11-24
- Posts: 455

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 12,919

Well done, irspow!

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 12,919

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.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 12,919

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.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 12,919

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?

Character is who you are when no one is looking.

Offline

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

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 12,919

Answer to M # 8:-

Perfectly correct, Janefairfax!

Character is who you are when no one is looking.

Offline

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'

'Humanity is still kept intact. It remains within.' -Alokananda

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 12,919

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?

Character is who you are when no one is looking.

Offline