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Mathematics 68 Online
OpenStudy (anonymous):

Who is able to solve this difficult question!!! Open cones are made from nets cut from a large sheet of paper 1.2m x 1.0m. If a cone has a radius of 6cm and a slant height of 10cm, how many cones can be made from the sheet? (Assume there is negligible wastage of paper.)

jimthompson5910 (jim_thompson5910):

Hint: the lateral surface area of a cone is LSA = pi*r*s where pi = 3.14 (roughly) r = radius of cone s = slant height of cone

OpenStudy (anonymous):

R is given as 6cm S is given as 10cm

OpenStudy (anonymous):

So in this question we aren't meant to use the formula SA=Pi(r)(s) + Pi(r)^2?

OpenStudy (anonymous):

Only the lateral SA?

jimthompson5910 (jim_thompson5910):

yes but this is an OPEN cone, so there is no base

jimthompson5910 (jim_thompson5910):

so this is like an ice cream cone

OpenStudy (anonymous):

Okay now I get it. So after we get the answer of the LSA we divide the area of the sheet by LSA to see how many cones are made from the sheet?

jimthompson5910 (jim_thompson5910):

exactly

jimthompson5910 (jim_thompson5910):

this is if you somehow manage to squeeze the nets of the cones in an optimal fashion wasting as little paper as possible

OpenStudy (anonymous):

I've got another question that has been bugging me for quite a long time

jimthompson5910 (jim_thompson5910):

ok

jimthompson5910 (jim_thompson5910):

what is it

OpenStudy (anonymous):

It's somehow related

OpenStudy (anonymous):

If the surface area of a sphere to a cylinder is in the ratio 4:3 and the sphere has a radius of 3a, calculate the radius of the cylinder if the radius of the cylinder is equal to its height

jimthompson5910 (jim_thompson5910):

The sphere has a radius of 3a, so r = 3a and the surface area is SA = 4*pi*r^2 SA = 4*pi*(3a)^2 SA = 4*pi*9a^2 SA = 36a^2*pi

jimthompson5910 (jim_thompson5910):

the surface area of a sphere to a cylinder is in the ratio 4:3 so (SA of Sphere)/(SA of Cylinder) = 4/3 (36a^2*pi)/(SA of Cylinder) = 4/3 3*(36a^2*pi) = 4(SA of Cylinder) 108a^2*pi = 4(SA of Cylinder) SA of Cylinder = 108a^2*pi/4 SA of Cylinder = 27a^2*pi

jimthompson5910 (jim_thompson5910):

SA of Cylinder SA = 2*pi*r^2 + 2*pi*r*h SA = 2*pi*r^2 + 2*pi*r*r .... height = radius SA = 2*pi*r^2 + 2*pi*r^2 SA = 4*pi*r^2 27a^2*pi = 4*pi*r^2 solve for r

OpenStudy (anonymous):

Mate you don't know how much I appreciate your help

OpenStudy (anonymous):

I posted these questions a few times but nobody knew how to answer them

OpenStudy (anonymous):

I'm going to reward you a medal

jimthompson5910 (jim_thompson5910):

you're welcome

OpenStudy (anonymous):

To be sure is the answer r=3a square root of 3 /2 ???

jimthompson5910 (jim_thompson5910):

27a^2*pi = 4*pi*r^2 27a^2 = 4*r^2 (27a^2)/4 = r^2 r^2 = (27a^2)/4 r = sqrt( (27a^2)/4 ) r = (3a/2)*sqrt(3) so you are correct

OpenStudy (anonymous):

The answer in the textbook must be incorrect

jimthompson5910 (jim_thompson5910):

what does it say

OpenStudy (anonymous):

It has as an answer r=3*square root of 3a /2

jimthompson5910 (jim_thompson5910):

\[\Large r = \frac{3\sqrt{3a}}{2}\] or \[\Large r = \frac{3\sqrt{3}a}{2}\]

jimthompson5910 (jim_thompson5910):

basically I'm asking if the 'a' is in the square root or not

OpenStudy (anonymous):

The second one

jimthompson5910 (jim_thompson5910):

then you can rearrange the terms to get \[\Large r = \frac{3\sqrt{3}a}{2}\] \[\Large r = \frac{3a\sqrt{3}}{2}\]

jimthompson5910 (jim_thompson5910):

which is the same as what we got

jimthompson5910 (jim_thompson5910):

bad use of notation though

OpenStudy (anonymous):

A is in it. I guess they made a slight mistake

jimthompson5910 (jim_thompson5910):

oh 'a' is in the square root?

OpenStudy (anonymous):

Yeh

jimthompson5910 (jim_thompson5910):

maybe it's a typo or they didn't mean to write it in the root

jimthompson5910 (jim_thompson5910):

it should be outside though

OpenStudy (anonymous):

I agree

OpenStudy (anonymous):

I'm going through a lot of these questions. They are sometimes tricky and hard to figure out

jimthompson5910 (jim_thompson5910):

yeah i would just bring it up with the teacher and see what s/he says about it

OpenStudy (anonymous):

Yeah I should. Thanks a lot any ways

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