calculator conundrum (1 Viewer)

[coolboy234]

Ok guys, you probably know me by the guy who has asked 4 maths questions already but this thread has something to do with the calculator. In question 1 (refer to MXE2 Maths Questions Help!!), when i asked the question, " Find the length of the side of a regular octagon that has area 500 cm squared",

When Bored of SC, wrote out the step as ( a squared = 125/sin 45) to get 176.7766, i apparently had got a squared = 146.9026704, and not a squared to be 176.7766. Anywayz, when I had used the sine rule to get the side of the octagon, the answer was negative and not Bored of Sc's answer which was approximately 10cm. I got the negative answer of -11.32810165.

So is there something wrong with my calculator???

Btw, there's one last question which has not been solved yet, SO CAN YOU SOLVE IT?

3. A water cooler has cone-shaped paper drinking cups. The volume of a cone can be found using this formula: V = (Pi x radius squared x height) divided by 3
Anton pours water into a cup until it contains water to half of its volume.
What is the depth of the water, to the nearest millimetre, in the cup?
http://community.boredofstudies.org/attachment.php?attachmentid=16758&stc=1&d=1216635986



Thanks in advance, coolboy234

 

[tacogym27101990]

your calculators in radians
and the 45 is degrees change ure calc to degrees of instead of 45 use pi/4

 

[bored of sc]

Volume of water in cup half full = (Pi x r² x h)/6
= (pi x 30² x 150)/6
= 70686mm³

Then do using the same formula put in the volume as 70686 and the height to radius is in the ratio 5:1. (150/30)

So then do 70686 = (Pi x 1a² x 5a)/3

Then solve for a.

70686 = [Pi x a² x 5a]/3
212058 = pi x 5a³
a³ = 212058/5pi
a = cube root (70686x3/5pi)
a = 23.8mm (to 1.d.p)

Now that we know the radius is 23.8mm multiply by 5 since the ratio of the height to radius is 5:1. (Thanks tacogym27101990)

23.8 x 5
= 119 mm

 

[coolboy234]

bored of sc, your right again , thanks for the solution!!!
















thanks, coolboy234

 

[tacogym27101990]

Volume of water in cup half full = (Pi x r² x h)/6
= (pi x 30² x 150)/6
= 70686mm³

Then do using the same formula put in the volume as 70686 and the height to radius is in the ratio 5:1. (150/30)

So then do 70686 = (Pi x 1a² x 5a)/3

Then solve for a.

70686 = [Pi x a² x 5a]/3
212058 = pi x 5a³
a³ = 212058/5pi
a = cube root (70686x3/5pi)
a = 23.8mm (to nearest mm)

Now that we know the radius is 23.8mm --> sub this again back into equation for volume of water this time calling depth (height) b.

70686 = (pi x 23.8² x b)/3
212058 = pi x 566.44 x b
b = (70686 x 3)/(pi x 566.44)
b = 119.1655918...
= 119 mm (to nearest mm)

Got a funny feeling that is WAY OFF but.

nice work
but u realise you didnt need the last 5 lines
after u realised the ratio of height:rad = 5:1
and u found the radius you couldve just multiplied it by 5

 

[lolokay]

lol you only need one line really

150/[2^(1/3)] =~ 119
since radius is proportional to height, h₁³ = 2h₂³

 

[bored of sc]

lol you only need one line really

150/[2^(1/3)] =~ 119
since radius is proportional to height, h₁³ = 2h₂³

Care to elaborate?

 

[bored of sc]

nice work
but u realise you didnt need the last 5 lines
after u realised the ratio of height:rad = 5:1
and u found the radius you couldve just multiplied it by 5

No, I didn't realise. Cheers.

 

[lolokay]

Care to elaborate?

height of the water is proportional to the radius of the section filled at any point
say radius/height = k
then the formula for volume of a cone is 1/3 *pi*k^2*h^3
which can be expressed as bh^3, where b is a constant
so we have: b*150^3 = 2b*h^3
h = 150/[2^(1/3)] =~119

 

[bored of sc]

height of the water is proportional to the radius of the section filled at any point
say radius/height = k
then the formula for volume of a cone is 1/3 *pi*k^2*h^3
which can be expressed as bh^3, where b is a constant
so we have: b*150^3 = 2b*h^3
h = 150/[2^(1/3)] =~119

Wow you are ridiculously GOOD at maths.

 

[lolokay]

thanks