3 solid spheres of radius 2 m, 1 solid cylinder of radius 3 m, height 4 meter and 2 solid cones of r

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06 Sep 2017 Radius and Volume

3 solid spheres of radius 2 m, 1 solid cylinder of radius 3 m, height 4 meter and 2 solid cones of radius 4 m, height 3 m are melted to form a bigger solid sphere. What is the radius of this bigger solid sphere in meters?

OPtion

1) 4.22
2) 4.14
3) 4.46
4) 4.01
5) 4.47
6) 4.27
7) 3.73
8) 3.66
9) 3.58
10)None of these

Solution

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

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

=> 4/3*R^3 = 4*8 + 36 + 32 = 100
=> R^3 = 75
R = 75^(1/3) = 4.217 =~4.22 m

Option 1)

Correct Option: 1 Best Solution (10)

AYAN PAUL   7 years AGO

Volume of Sphere is (4/3)*22/7*r^3 Volume of Cylinder is (22/7)*r^2*h and volume of cone is (1/3)*22/7*r^2*h
Now if we replace r and h from above question we can find that total volume will be 100 * 22/7
Now volume of sphere = (4/3)*22/7*r^3 = 100*22/7
solving these we get r = 4.22 m

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Varun   7 years AGO

Volume of sphere = 4/3 pi r ^ 3
Volume of cylinder = pi h r^2

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atheesh padala   7 years AGO

sum of all volumes is 314
then the radius is 4.217~4.22

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Santanu Bera   7 years AGO

4/3 π r^3 = (Volume of Three Solid sphere ) + (volume of one solid cylinder ) + (Volume of two solid cones )

the actual answer is 4.217 so we can write 4.22

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Abhijith Sankar E U   7 years AGO

vol. of sphere = 4/3*pi*2^3
vol. of cyl = pi*3^2*4
vol. of cone = 1/3*pi*4^2*3
vol .of big sphere =4/3*pi*r^3
since 3 solid spheres and 2 sold cones
r= 4.22

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Anupam Tripathi   7 years AGO

4/3pi*r^3=3*(4/3)*pi*r^3+1*pi*r*r*h+2*(1/)*pi*r*r*h
4/3pi*r^3=4*pi*8+pi*36+32pi
Now, 4/3pi*r^3=100pi
r^3=75
r=4.22

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Riya malaiya   7 years AGO

area of 3 sphere + area of one cylinder+ area of 2 cone = area of big sphere
32pi + 108pi + 32pi = 4/3 pi r^3
r = 4.22 m

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raksha s shetty   7 years AGO

volume of 3 sphere balls=32pi
volume of cylinder =36pi
volume of 2 cone=32pi
total volume=100pi
volume of bigger sphere =4/3*pi*r^3=100pi
therefore r=4.22m

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Ashwani Kumar   7 years AGO

Find the volume of a sphere(4/3 (pi)*r^3), cylinder (2pi r^2 h)and cone(pi r^2 (h/3))
Add them.
and divide it to 4/3 pi
the result is R^3 = 75
so R=4.217 aproxx 4,22

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Md Arzoo Azim   7 years AGO

Sum of volume of all is equal to volume of bigger sphere from there find the radius.

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