Maths Problem

[Shutpa]

Hi, could somebody please help me solve this?

A circular piece of card, with radius of 12cm, has a quarter of it removed and is folded to form a cone. The slanted height of the cone is 12cm and the vertical height is h cm.

Show that the volume of the cone, Vcm^3, is given by the expression V = 1/3 (3.14h)(144-h^2)

(^ to the power of)

URGENT!

 

[pred]

"Peice of Pie"

 

[Shutpa]

"Peice of Pie"

 

[Norcon]

Hippotomas therom.

 

[Susiejb]

sorry Bolo I only know about mince pies

 

[HERTS P&D]

And the answer is 1/2 litre.

Andy

 

[cantaloup63]

Two methods:

(A) Original piece of card has circumference 24pi (pi x diameter)
Quarter of it removed means that the circumference of the base of the cone is 3/4 of 24pi = 18pi

So the radius of the base of the cone = 18pi divided by 2pi (since circumference =2xpixR) = 9

Now the volume of a cone = 1/3 area of base x height
= 1/3 x pi x 9^2 x h
= 1/3 x pi x 81 x h
= pi x 27 x h

(B) The way you have wirtten it is slightly different - using pythagoras, the radius of the cone is squareroot of (12^2-h^2)
So the area of the base is pi x r^2
= pi x (144-h^2)

But volume of a cone is (as previosuly stated) 1/3 area of base x height
= 1/3 x (pi x (144-h^2)) x h
= 1/3 (3.14h)(144-h^2)
which is what you required


Since both (A) and (B) must give you the same answer, if you equate the two expressions then you would be able to find the height of the cone, if you so wish

 

[Shutpa]

And the answer is 1/2 litre.

Andy

No! The proof is:

The slanted height can be considered the hypotunse of a right-angle triangle with the radius of the base of cone and vertical height forming the other sides,so by pythagorean theorem 12^2=h^2 +r^2.Thus r^2=144-h^2

V=1/3(h)(r^2)3.14



PS Thank you for your unvaluable help.

 

[ColJack]

Two methods:

(A) Original piece of card has circumference 12pi (pi x diameter)

i thought he said the radius was 12? making the diameter 24...

 

[cantaloup63]

Two methods:

(A) Original piece of card has circumference 12pi (pi x diameter)

i thought he said the radius was 12? making the diameter 24...

That's what I said

 

[Blasphemous]

And the answer is 1/2 litre.

Andy

No! The proof is:

The slanted height can be considered the hypotunse of a right-angle triangle with the radius of the base of cone and vertical height forming the other sides,so by pythagorean theorem 12^2=h^2 +r^2.Thus r^2=144-h^2

V=1/3(h)(r^2)3.14



PS Thank you for your unvaluable help.

No 'thanks' for cantaloup63?

 

[joinerjohn]

Two methods:

(A) Original piece of card has circumference 12pi (pi x diameter)

i thought he said the radius was 12? making the diameter 24...

That's what I said

Ahh Canta, you've been caught out mate. Did you let your dad do your homework again??

My school report for Maths said,, "John is not getting better at maths, but I'm glad to see his father is improving with John's homework."


Seriously though, up until about halfway through the third year at secondary school, maths was one of my weakest subjects, then suddenly I picked up at it and it was just like a light was turned on in my brain. I ended up being the top of the school in exam results at 16.
Pity I've forgotten most of it now.

 

[cantaloup63]

No 'thanks' for cantaloup63?

In fairness I did make a bit of a horlicks by misreading it a bit