Latest L&T Aptitude Question SOLUTION: A right circular cylinder and a cone are there. Base radius of cone is equal to radius of cylinder. What is the ratio of height to slant side if their volume are the same?

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A right circular cylinder and a cone are there. Base radius of cone is equal to radius of cylinder. What is the ratio of height to slant side if their volume are the same?

Asked In L&T vishnupriya.O (11 years ago)

Unsolved Read Solution (9)

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Read Solution (9) :

Garima  (11 years ago)

1/3 pi r^2 h1 = pi r^2 h2
h1/h2= 3/1

height of cone : height of cylinder = 3:1

Is this solution Helpfull? Yes (18) | No (21)  

jaswinder  (10 years ago)

since there volume are same then :
pi*(r)square*h=(1/3)*pi*(r)square*h which gives 1:3

Is this solution Helpfull? Yes (9) | No (10)  

sravan  (10 years ago)

They have asked the ratio of cylinder to the cone
so Cylinder volume is pi*r^2*h
cone volume is 1/3*pi*r^2*l
cylinder/cone=h/l=1/(1/3)=3/1==3:1

Is this solution Helpfull? Yes (4) | No (12)  

THUMMALA VINEESHA  (8 years ago)

cylinder=pi*r^2*h1
cone=(1/3)*pi*r^2*h2
pi*r^2*h1=(1/3)*pi*r^2*h2
h1/h2=1/3

Is this solution Helpfull? Yes (3) | No (2)  

Suman kumar  (8 years ago)

pi*r^2*h1 = 1/3 *pi *r^2 *h2
so, h1 / h2 = 1:3

Is this solution Helpfull? Yes (1) | No (3)  

Nikhil More  (9 years ago)

Slant height = (r^2 + h^2)^(1/2)
h1/h2=3:1

Is this solution Helpfull? Yes | No (3)  

sonam  (8 years ago)

slant side means inclined of cone.so the ratio of height of cylinder to the slant side is
h1=x/2*3.14*r and h2=x/3.14&r,
h1:h2=2:1,where x is surface area because radius is equal & only height is different.so
ans is 2:1

Is this solution Helpfull? Yes | No (1)  

BHARAT KUMAR  (7 years ago)

cylinder=pi r^2 h1
cone=1/3 pi r^2 h2
h2/h1 =3 : 1

Is this solution Helpfull? Yes | No (1)  

Pravalika  (4 years ago)

Volume of a cylinder = (pi)r^2*h(cylinder).

Volume of a cone = (1/3)(pi)r^2*h(cone).

Since volumes are the same, h(cylinder)= (1/3)(cone, or

h(cone) = 3h(cylinder).

Slant height of cone = [r^2 + h(cone)^2]^0.5 = [1 + h(cone)^2]^0.5

= [1 + {3h(cylinder)}^2]^0.5

Hence, ratio of height of cylinder to slant height of cone =h(cylinder) : [1 + {3h(cylinder)}^2]^0.5 .

If h(cylinder) is taken as unity, then ratio of height of cylinder to slant height of cone =1 : [1 + 3^2]^0.5 = 1:√10.

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