M4maths Previous Puzzles

08 Aug 2017 Radius and Volume

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

OPtion

1) 10.22
2) 11.14
3) 12.09
4) 11.24
5) 10.89
6) 11.09
7) 12.09
8) 10.94
9) 12.04
10)None of these

Solution

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

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

=> 4/3*R^3 = 4*343 + 5*75 + 7*21 = 1894
=> R^3 = 1420.5
R = 1420.5^(1/3) = 11.24 m

Option 4)

Correct Option: 4 Best Solution (14)

G.S.Kantharao   7 years AGO

Radii are 7m,5m,3m
Heights are 3m,7m
No of solids are 3,5,7
Total volume= 3*4*π*(7^3)/3 + 5* π*(5^2)*3+7*π*(3^2)*7/3
=(1372π+375π+147π)m^3
4*πR^3/3=1894πm^3
R=(1894*3/4)^(1/3)=11.24m
Hence the right option is 4👈

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Mukund Manohar   7 years AGO

Volume of bigger solid sphere = (3*1436.76)+(5*235.62)+(7*65.97)
= 4310.28 + 1178.1 + 461.79
= 5950.17 m^3
Radius of the bigger solid sphere = cube root(1419.93)
= 11.24 m

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SAYAN CHATTERJEE   7 years AGO

(3*4/3*3.14*7^3+5*5^2*3+7*1/3*3.14*3^2*7)=4/3*3.14*R^3
=> R= 11.24.
Option 4.

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Harshal Sapkade   7 years AGO

by melting all the solids we get there volumes. by applying the formulas for particular cubes we can get the answer.

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shreya   7 years AGO

vol of sphere×3 + vol of cylinder×5 + vol of cone×7 = vol of sphere
1894π = 4π r ^3 / 3
r=11.24

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Ravi   7 years AGO

add all the volumes of sphere, cylinder and come and put equal to the big solid sphere volume which is 4/3πr^3 so the r will be equal to 11.24

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KRISHNAKUMAR   7 years AGO

the volume of 3 sphere is = 4310.28
the volume of 5 cylinder is =1178.1
the volume of 7 cone is=461.79
the volume of new cone is=4310.28+1178.1+461.79
=5950.74
from above value radius is=11.2397

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Madhuvani v   7 years AGO

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

Here r1=7m, r2=5m, r3=3m, h1=3m, h2=7m, and R=?
Volume of Larger Sphere = Volume of 3 smaller sphere's + Volume of 5 Cylinder +Volume of 7 Cones
=> (4/3)*Pi*R^3 = 3*(4/3)*Pi*r1^3 + 5*P1*r2^2*h1 + 7*(1/3)*Pi*r3^2*h2
(4/3)*pi*R^3 = 1372*pi+375*pi+147*pi
=> 4/3*R^3 = 1894pi
=> R^3 = 1420.5
R =cube root(1420.5) = 11.24 m

Option 4)

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Samiksha Sonam   7 years AGO

Area of bigger sphere=3*[(4/3)*(22/7)*343]+5*[(22/7)*25*3]+[7*(1/3)*(22/7)*9*7]=5952.6
Radius of bigger sphere=11.24

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Harshit Gupta   7 years AGO

The basic concept for this is that Total Volume remains the same when all the solid spheres, solid cylinders and solid cones are added up to form a single solid sphere.

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Ramkumar saini   7 years AGO

3*1436.76=4310.08
5*235.62=1178.1
7*65.97=461.79
r^3=1419.16
r=11.2376

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AYAN PAUL   7 years AGO

Here the equation become (4/3)*22/7*r^3 = 3*(4/3)*22/7*343 + 5*(22/7)*25*3 + 7*(1/3)*(22/7)*9*7
Solving this equation we get that r = 11.24 m

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palak Jain   7 years AGO

volume of 3 spheres=4/3(pie)*r^3 where r=7m=1372 pie m^3
volume of 5 cylinders=pie*r^2*h where r=5m,h=3m=375pie m ^3
volume of 7 solid cones=4/3 pie *r^2*h where r=3m ,h=7m=147 piem^3
total volume=1894 pie m^3
1894 pie m^3=4/3 pie r^3
r=11.24 m

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Abinesh.R   7 years AGO

volume of sphere + volume of cylinders+volume of cone=volume of sphere..

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