Two metallic right circular cones having their height 4.1 cm and 4.3 cm and the radii of their bases

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17 Jun 2016 Diameter of sphere

Two metallic right circular cones having their height 4.1 cm and 4.3 cm and the radii of their bases 2.1 cm each, have been melted together and recast into a sphere. The diameter of the sphere is

OPtion

1) 4.2 cm
2) 4.8 cm
3) 2.5 cm
4) 1.4 cm
5) 1.8 cm
6) 3.9 cm
7) 3.5 cm
8) 5.8 cm
9) 6.3 cm
10)None of these

Solution

Sum of the volume of the cones = volume of the sphere
1/3*Pi*2.1^2*4.1 + 1/3*Pi*2.1^2*4.3 = 4/3*Pi*R^3
Solve
Diameter = 4.2 cm

Option 1)

Correct Option: 1 Best Solution (22)

KUMAR HARSH   8 years AGO

vol of sphere =vol of 2 cones
4/3*pi*r^3=pi*2.1(4.1/3+4.3/3)
r^3=2.1^3
r=2.1
diameter of spere is 2.1*2=4.2

Like? Yes (4) | No (1)  

RAHUL KUMAR   8 years AGO

Given that, volume of sphere =
volume of two cones
Here, volume of two cones = 1/3 x pi x (2.1)^2 x 4.1 + 1/3 x pi x (2.1)^2 x 4.3
=> 1/3 x pi x (2.1)^2 x 8.4
Let the radius of the sphere be R.
Then 4/3 x pi x R^3 = 1/3 x pi x (2.1)^2 x 8.4
4 x R^3 = (2.1)^2 x 2.1 x 4
4 x R^3 = (2.1)^3 x 4
R = 2.1
Hence, the diameter is 4.2 units.

option (1)

Like? Yes (4) | No (2)  

Tarun Kumar   8 years AGO

Volume of sphere = sum of the volume of the cones
4/3 * pi * r^3 = 1/3 * pi * 2.1*2.1 * 4.1 + 1/3 * pi * 2.1 *2.1 * 4.3
4/3 * pi * r^3 = 1/3 * pi * 2.1 * 2.1 * 8.4
r^3 = (2.1 * 2.1 * 8.4 ) / 4 = 2.1 * 2.1 * 2.1
therefore radii of sphere = 2.1 cm
so , diameter of the sphere = 2 * 2.1 = 4.2 cm

Like? Yes (3) | No (1)  

RISHABH   8 years AGO

1/3*22/7*2.1*2.1(4.1+4.3) = 4/3*22/7*r^3
=>r =2.1cm
So, d= 2* 2.1 = 4.2 cm

Like? Yes (2) | No   

Althaf   8 years AGO

sum of the volumes of both right circular cone is equal to the volume of the sphere. .
so,
volume of first right circular cone=(pi*r*r*h)/3
= 36.97 cm^3
second right circular cone = 40.66 cm^3
total volume = 77.63 cm^3
now, sphere volume = (4/3)*pi*r^3
= 38.79 cm^3
hence, r= 2.1cm => d=4.2cm. . .

Like? Yes (1) | No (1)  

Aakash Beniwal   8 years AGO

1/3 * pi * r ^2 * ( h1 + h2 ) = 4/3 * pi * R^3
here r= 2.1, h1=4.1 , h2=4.3 , R= radius of sphere
Diameter = 2 * R
ans is 4.2

Like? Yes (1) | No (1)  

vikas rana   8 years AGO

here r1=r2=2.1cm
h1=4.1 cm,h2=4.2cm
volume of sphere=4/3 *pi*r^3
volume of two cones=1/3 *pi*r1^2*h1 + 1/3* pi*r2^2*h2
equating both volumes
we get r=2.1 cm
diameter=2.1*2=4.2 cm
option(1)

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Manvi   8 years AGO

the volume will remain the same. so, equating the two gives radius which is doubled to obtain the requisite diameter.

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Alex   8 years AGO

volume of first cone = (1/3 * pi * (2.1)^2 * 4.1 ) = 18.942 cm^2
volume of second cone = (i/3 * pi * (2.1)^2 * 4.3 ) = 19.866 cm^2
Total volume = 18.942 + 19.866 = 38.808 cm^2
(4/3 * pi * r^3 ) = 38.942
hence, r = 2.1 cm
d= 2*r = 2.1*2 = 4.2cm

Like? Yes (1) | No (1)  

ABHINAV PUSHPAM   8 years AGO

Given that, volume of sphere =
volume of two cones
Here, volume of two cones = 1/3 x pi x (2.1)^2 x 4.1 + 1/3 x pi x (2.1)^2 x 4.3
=> 1/3 x pi x (2.1)^2 x 8.4
Let the radius of the sphere be R.
Then 4/3 x pi x R^3 = 1/3 x pi x (2.1)^2 x 8.4
4 x R^3 = (2.1)^2 x 2.1 x 4
4 x R^3 = (2.1)^3 x 4
R = 2.1
Hence, the diameter is 4.2 units.

Like? Yes (1) | No (1)  

Kumar Navendu   8 years AGO

total volume of cones = volume of sphere
pi*r*r*(h1 + h2)/3 = 4*pi*R*R*R/3

=> R = 2.1 cm
so d=4.2 cm

Like? Yes (1) | No (1)  

rahul patidar   8 years AGO

sum of the volume of two cones are equal to the volume of sphear

Like? Yes | No (1)  

D.sai maniveer   8 years AGO

as we know volume of sphere depends on radius .
here radius of cone is 2.1 cm.
then diameter of sphere is =2r=2*2.1 =4.2 cm

Like? Yes | No (1)  

RAVAL   8 years AGO

total volume of cone = 1/3 * pi * 2.1^2 * (4.1+4.3)
= 38.4044 cm^3
so, 38.4044 = volume of sphere = 4/3 * pi * (d/2)^3
diameter of sphere = 4.19cm = 4.2 cm

Like? Yes | No (1)  

Ramesh Viswanatham   8 years AGO

vol of sphere=4/3*pi*r^3
vol of cone 1/3*pi*r^2*h
by this we can get radius of sphere i.e., 2.1
so diameter is 4.2

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BRINDHA P   8 years AGO

Volume of sphere = Volume of 2 cones = (1/3 π x (2.1*2.1) x 4.1+ 1/3 π x (2.1)2 x 4.3) =1/3π×(2.1)*(2.1)(8.4)
Let the radius of sphere be R
4/3 π R3 = 1/3π(2.1)3or R = 2.1cm
Hence , diameter of the sphere = 4.2 cm

Like? Yes | No (1)  

NEHA BANR   8 years AGO

let height of respective cones be h1 and h2 . radius of the cased sphere be R. radius of cone be r.
volume after recasting will remain same.
Therefore, the volume of two cones is equal to the volume of sphere.
1/3(pi)*r^2*[h1^2+h2^2]=4/3*pi*R^3
therefore, R=2.1cm.
Diameter=2*R
=4.2 cm.
Option 1.

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Shafigheh Nikpour   8 years AGO

volume of right circular cone=(1/3)*PI*radii^2*height
PI=22/7
volume of cone(1)=(1/3)*(22/7)*2.1^2*4.1=18.942
volume of cone(2)=(1/3)*(22/7)*2.1^2*4.3=19.866
volume of sphere=18.942+19.866=38.808
volume of sphere=(4/3)(PI)r^3=(4/3)*(22/7)*r^3=38.808
so r=2.1 and diameter=4.2

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ABHISHEK KUMAR   8 years AGO

4/3?r^3 = 1/3?r^2(h1 +h2)
ie. r^3= (2.1)^3
ie. r= 2.1
ie. d=4.2

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rohit jain   8 years AGO

sum of volumes of both the cones is equal to volume of sphere.

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sam   8 years AGO

volume of two cones = volume of sphere

(1÷3)*(22/7)*(2.1)*(4.1+4.3)=(4÷3)*(22÷7)*(R^3)
R = 2.1

Like? Yes | No (1)  

M.R. Satheesh Kumar   8 years AGO

Let radius be r. Vol of sphere = vol. of two cones
4/3*pi*r^3 = (pi/3)*4*2.1^3
r=2.1cm
d=4.2cm

Like? Yes | No (1)