11 solid spheres of radius 3 m, 9 solid cylinder of radius 4 m, height 5 meter and 13 solid cones of

M4maths Previous Puzzles

18 May 2017 Radius and Volume

11 solid spheres of radius 3 m, 9 solid cylinder of radius 4 m, height 5 meter and 13 solid cones of radius 2 m, height 4 m are melted to form a bigger solid sphere. What is the radius of this bigger solid sphere in meters?

OPtion

1) 9.22
2) 10.02
3) 9.62
4) 8.98
5) 9.89
6) 10.09
7) 8.79
8) 10.04
9) 8.62
10)None of these

Solution

Volume of 11 smaller sphere's = 11*(4/3)*Pi*r1^3
Volume of 9 Cylinder = 9*(Pi*r2^2*h1)
Volume of 13 Cones = 13*(1/3)*Pi*r3^2*h2
Volume of Larger Sphere = (4/3)*Pi*R^3

Here r1=3m, r2=4m, r3=2m, h1=5m, h2=4m, and R=?
Volume of Larger Sphere = Volume of 11 smaller sphere's + Volume of 9 Cylinder +Volume of 13 Cones
=> (4/3)*Pi*R^3 = 11*(4/3)*Pi*r1^3 + 9*P1*r2^2*h1 + 13*(1/3)*Pi*r3^2*h2

=> 4/3*R^3 = 4*99 + 9*80 + 13*16/3 = 1185.333
=> R^3 = 889
R = 889^(1/3) = 9.62 m

Option 3)

Correct Option: 3 Best Solution (7)

G.S.Kantharao   7 years AGO

Volumes of solids = (11*4π*27)/3 + (9*π*80)+(13*π*16)/3 = (4*π*889)/3
Volume of sphere (4*π*R^3)/3=(4*π*889)/3
R^3=889
R=(889)^1/3=9.62mts.approximately.
Hence the right option is 3.👈

Like? Yes (1) | No   

Haritha Mummidivarapu   7 years AGO

volume of sphere = 4/3 *(pi * r ^3)
therefore, total volume of 11 spheres of radius = 3 is
total volume of spheres = 11 * 4/3 * pi * 3 ^3
= 1244.0706
volume of cylinder = pi * r^2 * h
total volume of 9 cylinders of r=4 and h = 5,
= 9 * pi*4^2 * 5
= 2261.94
volume of cone = 1/3 * pi * r^2 *h
total volume of 13 cones of r=2 , h=4 is
= 13 /3 * pi * 2^2 * 4
= 217.817

therefore total volume of all solids = 3723.827
so volume of large sphere = 3723.827
=> 4/3 * pi * r^3 = 3723.827
=> r = 9.62 mts

Like? Yes (1) | No   

Mukund Manohar   7 years AGO

Volume of bigger solid sphere = Volume of (11 solid spheres + 9 solid cylinders + 13 solid cones)
= 396*pi + 720*pi + {(208*3)/pi}
= (3556/3)*pi
Let the required radius be R meters
Now, (4*pi*R^3)/3 = (3556/3)*pi
=> R = cube root (3556/4)
= cube root (889)
= 9.62 m

Like? Yes | No   

Rakesh Kumar   7 years AGO

11*volume of sphere+9*volume of cylinder+13*volume of cones=volume of big sphere
11*4/3*3*3*3+4*4*5*9+1/3*2*2*4*13=4/3R^3
R=9.62

Like? Yes | No   

Amarnath Kumar Upadhyay   7 years AGO

4/3*22/7*r1^3+22/7*r2^2*h1+1/3*22/7*r3^2*h2=4/3*22/7*R^3

here value of r1 r,2, r3 ,h1,h2 is given
on solving we get R=9.6153 m

Like? Yes | No   

Lakshmi Durga   7 years AGO

sphere volume - 4/3 pi *r^3
cylinder volume -pi*r^2*h
cone volume -1/3 pi*r^2*h
11*s.v+9*c.v+13*cone volume=4/3pi*r^3
solving above equation r=9.615

Like? Yes | No   

palak Jain   7 years AGO

11 solid sphers=396pie
9 solid cylinder =720pie
13 solid cones=208pie/3
4/3pie r^3=1116pie+208pie/3
r^3=889
r=9.22

Like? Yes | No