The curved surface area of a cylinder is 24/7 times the total flat surface area(top +bottom).If the biggest possible cone is cut out from the cylinder, what is the ratio of the curved surface area of the cone to its flat surface area?
A) 24/7
B) 25/7
C) 27/7
D) 29/7
E) 30/7
A. 24/7
How did u get that, pls explain.
GMAT Team, howcome you’ll havent put up the answers to this?
Dear Sunitha,
Still waiting for someone to attempt, So that we can post reply.
Ans is B 25/7
answer is 25/7
IF The curved surface area of a cylinder is 24/7 times the total flat surface area(top +bottom), we get : pi (R^2) H= 24/7 (2 pi R)
so H/ R= 24/7…..[1]
If the biggest possible cone is cut out from the cylinder, it has radius and height same as cylinder. Curved surface area of cone is pi R L, where L is the slant height. L^2 = R^2 + H^2 ..[2] by Pythogaurus..
So ratio of the curved surface area of the cone to its flat surface area is (pi R L) / (pi R^2)= L/R
From [2] above, L^2/ R^2 = 1 + (H^2/R^2)
So L/R= sqrt [ 1 + (H^2/R^2)]
Substituting H/R from [1], L/R= sqrt ( 1+ 576/ 49) = sqrt (625/49)= 25/7
A
Here is my appproach. Correct me if I am wrong.
We can assume that curved surface area is 24 and sum of two flat surface areas is 7. If we cut a cone of max possible height, it will have only one flat surface of the cylinder. so we can say its area is 7/2. if you imagine the curved portion of the cylindar as a flat sheet, it will look like a rectangle. To make a cone out of it, you have to cut a triangle out of that rectangle with one base of the rectangle as base of the triangle and mid point of the other base as third point of the triangle. Area of your new traingle will have exactly half of the rectangle i.e., 24/2. So ratio of curved surface area of the cone to its flat surface is 24/2/7/2 = 24/7. So ans A.
my approach was little bit off but still right.
third point of the triangle doesnt have to be mid point of the other base of the rectangle. it can be any point. Still, area of the rectangle is bh and area of the triangle is (1/2)bh. So it is still half of the area of the rectangle.
for mkorrapati
Your approach is right only problem is u were wrong when u calculated the area of cone using rectangle triangle concept. it holds true for Cylinder but not for Cone. it depends on the curved side of the triangle so 24/2 area for the cone is not correct.
for deepa,
your answer is same as it comes for me and to me it seems correct but your first statement is not correct.
it should be
2xpixrxh = 2×24/7xpixr^2
h/r = 24/7
else your approach seems correct and answer is B.
yes, varun,..that was a typo..
b
The answer is B – 25 / 7
But it takes me more than 5 minutes to solve it
The person who gets this on a real test could be heading for a 800.
Ans is B. 25/7 Solving time 7 mins.
2(pi)rh = (24/7) 2(pi)(r^2)
h/r = 24/7 –> (a)
To find –> [ (pi) r sqrt(r^2 + h^2) ] / [(pi) r ^2]
= sqrt(r^2 + h^2) / r
= l/r
Slant Height of a cone = l
l^2 = r^2 + h^2
l/r = sqrt( 1 + h^2/r^2 )
l/r = sqrt( 1 + 24^2/7^2 )
l/r = 25/7
The bottom line is I still cannot believe that this is an actual GMAT question.
Answer is B I took 3 min to solve especially h= (24/7) r . Only trick is biggest possible cone is that rest completely on the base so curved surface of cone is pi*r*l l is the slant height that is l*l=h*h + r*r
where h = height of cylinder and r base radius .
l*l=h*h + r*r = r*r + 625 8r*r/49 so l=(25/7) r
ratio of the curved surface area of the cone to its flat surface area=l/r
So answer is B
A is the answer
length of cone will be the Height of the cylinder
so rl/r^2=h/r=24/7
admin. what is the correct answer
A is the answer
length of cone will be the Height of the cylinder
so rl/r^2=h/r=24/7
admin. what is the correct answer?
B
Should be B
Take GMAT team, please provide the answer.
b
answer is B
all we need is find l/r ..i.e csa of cone/area of base
=> (pi *R *L)/(Pi * R* R)
From 1st equation : (2* Pi*R*H) /(2 *Pi* R*R)
we got H = 2* Pi
and L(Slant height of cone) = sqrt( H^2 + R^2)
..simple isn’t it
b all the way
25/7
B