2 solid spheres of radius 3 m, 3 solid cylinder of radius 2 m, height 3 meter and 2 solid cones of r

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12 Jul 2017 Radius and Volume

2 solid spheres of radius 3 m, 3 solid cylinder of radius 2 m, height 3 meter and 2 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) 4.17
2) 4.12
3) 4.46
4) 4.01
5) 4.87
6) 4.81
7) 3.73
8) 3.66
9) 3.58
10)3.51

Solution

Volume of 2 smaller sphere's = 2*(4/3)*Pi*r1^3
Volume of 3 Cylinder = 3*(Pi*r2^2*h1)
Volume of 2 Cones = 2*(1/3)*Pi*r2^2*h2
Volume of Larger Sphere = (4/3)*Pi*R^3
Here r1=3m, r2=2m, h1=3m, h2=4m, and R=?
Volume of Larger Sphere = Volume of 2 smaller sphere's + Volume of 3 Cylinders + Volume of 2 Cones
(4/3)*Pi*R^3 = 2*(4/3)*Pi*r1^3 + 3*P1*r2^2*h1 + 2*(1/3)*Pi*r2^2*h2
=> 4/3*R^3 = (8/3)*27 + 36 + 32/3
=> R^3 = 89
R = 89^(1/3) =4.46 m

Correct Option: 3 Best Solution (11)

Mukund Manohar   7 years AGO

Volume of bigger solid sphere
= (2*113.1) + (3*37.7) + (2*16.76)
= 226.2 + 113.1 + 33.52
= 372.82 m^3
Radius of the bigger solid sphere = cube root(88.97)
= 4.46 m

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SAYAN CHATTERJEE   7 years AGO

(2*4/3*3.14*3^3+3*3.14*2^2*3+2*1/3*3.14*2^2*4)= 4/3*3.14*R^3
hence, R= 4.46.
Option 3.

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Himanshu porwal   7 years AGO

4/3*3.14(54+27+8)=4/3*3.14*r^3
89=r^3
r=(89)^1/3
r=4.46

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AMAN Sinha   7 years AGO

first of all compute the volume of all shapes
vol of spere 4/3pie r^3
cyclinder= pie r^2h
cone =1/3 of cylinder
we add all volume.
total volume is 356/3 pie
now compute the radius using the formula of vol of sphere
radius is 4.46

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ALOKENDRA PAL   7 years AGO

total volume=(36π+72π+32/3π)
then let radius of new sphere is r
so volume is 4/3πr^3=total volume above
so, r=4.46

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Gokul Krishnan   7 years AGO

volume of (2 sphere+3 cylinder+2 cone)=volume of big sphere
on solving, 89=r^3
R=4.46 m

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Nabendu   7 years AGO

2(4π3^3/3)+3(π2^2*3)+2(1*π*2^2*4)=4π r^3/3
So,r^3=89. => r=4.46

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somannagari bhargavi   7 years AGO

calculate volume of everything and add then euating it to the volume of the sphere

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Rahul   7 years AGO

Sum of all given object volume = volume of bigger volume

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ajit bharti   7 years AGO

vol. of new sphare=2(vol. of old sphare)+2(vol. of cone)+3(vol. of cyliender)
4/3*pi*r^3=pi*(356/3)
therefore r^3=cube root of 89
r=4.46

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Shritansh   7 years AGO

Since volume of bigger sphere =89
Therefore 4/3πr ^3 = 89
Hence radius r= 4.46

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