5 solid spheres of radius 2 m, 7 solid cylinder of radius 3 m, height 7 meter and 4 solid cones of r

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22 Jun 2017 Radius and Volume

5 solid spheres of radius 2 m, 7 solid cylinder of radius 3 m, height 7 meter and 4 solid cones of radius 5 m, height 8 m are melted to form a bigger solid sphere. What is the radius of this bigger solid sphere in meters?

OPtion

1) 7.22
2) 9.14
3) 8.29
4) 9.01
5) 8.89
6) 7.99
7) 8.09
8) 8.66
9) 9.58
10)None of these

Solution

Volume of 5 smaller sphere's = 5*(4/3)*Pi*r1^3
Volume of 7 Cylinder = 7*(Pi*r2^2*h1)
Volume of 4 Cones = 4*(1/3)*Pi*r3^2*h2
Volume of Larger Sphere = (4/3)*Pi*R^3

Here r1=2m, r2=3m, r3=5m, h1=7m, h2=8m, and R=?
Volume of Larger Sphere = Volume of 5 smaller sphere's + Volume of 7 Cylinder +Volume of 4 Cones
=> (4/3)*Pi*R^3 = 5*(4/3)*Pi*r1^3 + 7*P1*r2^2*h1 + 4*(1/3)*Pi*r2^2*h2

=> 4/3*R^3 = 5*8*4/3 + 7*63 + 4/3*200 = 2283/3
=> R^3 = 570.75
R = 570.75^(1/3) = 8.29 m

Option 3)

Correct Option: 3 Best Solution (12)

Mukund Manohar   7 years AGO

Volume of bigger solid sphere = (33.51*5) + (197.92*7) + (209.44*4)
= 2390.75 m^3
Radius of bigger solid sphere = 8.29 m

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SAYAN CHATTERJEE   7 years AGO

5*4/3*3.14*2^3+7*3.14*3^2*7+4*1/3*3.14*5^2*8= 4/3*3.14*r^3
so, r= 8.29.
Option 3.

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G.S.Kantharao   7 years AGO

Radius of sphere =2m.
Radius of cylinder=3m
Height=7m
Base radius of cone =5m
Height=8m
Volumes are =(4*π*2^3)/3 , π*3^2*7,(π*5^2*8)/3
Sum of respective solid volumes= (4π/3)[5*(2^3)+(7*7*3^3)/4 + 5^2*8]
=(4π*/3)[40+(27*49)/4 +200]
=(4π/3)[(160+1323+800)/4]
=(4π/3)(2283/4)
=(4π/3)(8.29)^3
Solid Sphere =(4π/3)R^3=(4π/3)(8.29)^3
Radius =8.29m
Hence the Right option is 3☝

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Vishnu Prakash   7 years AGO

5*(4/3)*pi*8+7*pi*9*7+4*(1/3)*pi*25*8 = 2391.37

(4/3)*pi*r^3=2391.37

r^3=570.67

r=8.29

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ganesh chemanchula   7 years AGO

The combined equation will be
4/3pir^3=5[4/3pi(2)^3]+7[pi(3)^2(7)]+4[1/3pi(5)^2(8)]
by solving this we will get r^3=570.1
Then r=8.29
So option 3.

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Dhivya   7 years AGO

volume of sphere=(4*pi*r^3)/3
volume of cylinder=pi*r^2*h
volume of cone=(pi*r^2*h)/3
total volume produced=volume of five small spheres+volume of 7 cylinders+volume of 4 cones
=(4*pi*570.75*)/3
cuberoot(570.75)=8.29
Option:3

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rajat kushwaha   7 years AGO

volume of 5 sphere + volume of 7 cylinder + volume of 4 cone = volume of new sphere

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Amir Khan   7 years AGO

(5*volume of sphere) + (7*volume of cylinder) + (4*volume of cone) = volume of bigger sphere.

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Mohini Sikri   7 years AGO

Find the volumes of all the spheres,cylinders and cones. Add them all and equate with the final volume of the bigger cone. From there we can calculate the radius of bigger cone.

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AJAY SHOME   7 years AGO

volume of 5 sphere +volume of 7 cylinder+volume of 4 cone=volume of bigger sphere

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Abhijit Kumar Khanra   7 years AGO

volume of 5 solid spheres =5*(4/3)*pi*(2^3)
=167.551 m3
volume of 7 solid cylinder =7*pi*(3^2)*7
=1385.442 m3
volume of 4 cones=4*(1/3)*pi*(5^2)*8
=837.758 m3
Total volume when melted=2390.751 m3
So taking the radius of the bigger sphere as R,value of R is:
(4/3)*pi*R^3=2390.751
further calculation leads to R=8.29 m.

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Sourav Dass   7 years AGO

Sum of the volumes of spheres,cylinders and cones = volume of big sphere

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