2 solid spheres of radius 2 m and a solid cone of radius 2 m, height 2 m are melted to form a bigger

M4maths Previous Puzzles

11 Jan 2017 Radius of Sphere

2 solid spheres of radius 2 m and a solid cone of radius 2 m, height 2 m are melted to form a bigger solid sphere. What is the radius of this bigger solid sphere?

Please note that symbol ^ denotes power of

OPtion

1) 72^(1/3)
2) 54^(1/3)
3) 36^(1/3)
4) 18^(1/3)
5) (45/4)^(1/3)
6) (45/2)^(1/3)
7) (45/8)^(1/3)
8) 45^(1/3)
9) 18^(2/3)
10)36^(2/3)

Solution

Answer: 18^(1/3)
Volume of 2 smaller sphere's = 2*(4/3)*Pi*r^3
Volume of Cone = (1/3)*Pi*r^2*h
Volume of Larger Sphere = (4/3)*Pi*R^3
Here r=h=2m and R=?
Volume of Larger Sphere = Volume of 2 smaller sphere's + Volume of Cone
(4/3)*Pi*R^3 = 2*(4/3)*Pi*r^3 + (1/3)*Pi*r^2*h
=> 4*R^3 = (8*2^3 + 2^3) = 8*9
=> R^3 = 18
R = 18^(1/3)

Correct Option: 4 Best Solution (8)

madanpal vishwakarma    7 years AGO

Volume of sphere = 4/3 pi r^3 = 4/3* pi* 2^3 = 32pi/3

Volume of cone = 1/3 pi r^2 h = 1/3 * pi *2^2 * 2 = 8pi/3


As per question new sphere volume is the sum of three 2 Sphere and one cone = 2 * vol of sphere + vol of cone
Let the radius of new sphere is R

4/3 pi R^3 = 2[32pi/3]+8pi/3 =73pi/3

So R^3 =72/4
R= 18^ 1/3

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Karan   7 years AGO

Total volume= 2*(4/3)*(Pi)*(2)^3 + Pi*4*2/3= 24*Pi
If volume of new sphere is R, then
(4/3)*Pi* R^3= 24*Pi
R^3=18
R= 18^(1/3)

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chitransh mandhaniya   7 years AGO

2*(4/3*pie*2^3)+(1/3*pie*2^2*2)=4/3*pie*r^3;
r^3=18;
r=(18)^(1/3)

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Ajay Sharma   7 years AGO

volume of new sphere=volume of old sphere + volume of cone
=2*(4/3*22/7*2^3)+(22/7*4*2/3)
=1408/21+176/21=1584/21=4/3*22/7*r^3
r=18^1/3

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gubba ranjith kumar   7 years AGO

2*4/3*pi*2*2*2+1/3*pi*2*2*2=4/3*pi*18
=>r^3=18
=>r=18^(1/3)

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Sujata   7 years AGO

Volume of Sphere is (4/3)*pi*r^3
volume of cone is (1/3)*pi*r^2*h
So, we cam calculate respective volume, and find their sum. The volume of larger sphere is the sum of two sphere and one cone. Now. we can find radius using, same formula as,

pi/3*(2*4*8+8)=(4/3)*pi*r^3, so r = (18)^1/3

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P.Mohankumar   7 years AGO

Volume of solid sphere =(4/3)*π*r^3
For 2solid sphere with radiu 2m =(4/3)*π*(2^3)=66.99m^3
Volume of cone=(1/3)*π*r^2*h=(1/3)*π*(2^2)*2=8.37m^3
Volume of 2 solid sphere+volume of cone = biggest volume of cone
66.99+8.37=75.36m^3
(4/3)*π*r^3=75.36
Therefore r=(75.36/4.19)^3
=18^3

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nimisha gupta   7 years AGO

Volume of bigger sphere= 2*(vol of small sphere) +vol of cone
Vol of sphere=(4*pi*r^3)/3
Vol of cone=(pi*r^2*h)/3
Using this we get
Radius of bigger sphere=18^(1/3)

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