4 solid spheres of radius 1 m, 2 solid cylinders of radius 4 m, height 2 meter and 1 solid cone of r

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28 Feb 2018 Volume

4 solid spheres of radius 1 m, 2 solid cylinders of radius 4 m, height 2 meter and 1 solid cone 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) 3.08
1) 3.22
2) 3.14
3) 3.88
4) 3.80
5) 3.87
6) 3.27
7) 3.73
8) 3.83
9) 3.58
10)None of these

Solution

Volume of 4 smaller sphere's = 4*(4/3)*Pi*r1^3
Volume of 2 Cylinders = 2*(Pi*r2^2*h1)
Volume of 1 Cone = 1*(1/3)*Pi*r3^2*h2
Volume of Larger Sphere = (4/3)*Pi*R^3

Here r1=1m, r2=4m, r3=2m, h1=2m, h2=4m, and R=?
Volume of Larger Sphere = Volume of smaller sphere's + Volume of Cylinders +Volume of Cone
(4/3)*Pi*R^3 = 4*(4/3)*Pi*r1^3 + 2*P1*r2^2*h1 + 1*(1/3)*Pi*r3^2*h2

=> 4/3*R^3 = 4*(4/3)*1 + 2*16*2 + (1/3)*4*4 = (16/3) + 192/3 + 16/3
=> R^3 = 4 + 48 + 4
=> R^3 = 56
R = 3.826 m = ~ 3.83m


Option 8)

Correct Option: 8 Best Solution (0)