After melting 4 balls of iron of radius 2 cm., a larger ball is formed. Its radius is?

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18 Nov 2010 What will be the new ball radius?

After melting 4 balls of iron of radius 2 cm., a larger ball is formed. Its radius is?

OPtion

1) Less than 2 cm.
2) Greater than 4 cm.
3) 4 cm.
4) 2 cm.
5) Less than 4 cm.
6) 8 cm.
7) Greater than 8 cm.
8) Greater than 4 cm. but less than 8 cm.
9) 16 cm.
10) Greater than 16 cm.

Solution

According to mensuration, on melting 23 balls of 2 cm. radius, a ball of 4 cm. radius will be formed.

Correct Option: 5 Best Solution (7)

goutam Choudhury   13 years AGO

let the radius of new ball is r.volume of all four balls is 4/3#2^3*4. so the equation stands 4/3#2^3*4=4/3#r^3.This implies r^3=8*4=32.so the r be less than 4 and grater than 3.it satisfy option 5.

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Bimal   13 years AGO

If R is new radius , then

(4/3)*pi*R^3 = 4*(4/3)*pi*2^3 = 4*(4/3)*pi*8= 32*(4/3)*pi;... Then R = cuberoot 32 which is more than 3 but less than 4.

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SUDESHNA SEN   13 years AGO

Volume of 1 ball of iron of radius 2 cm
= (4/3)*(22/7)*(2^3)= (704/21)cubic cm
So, volume of 4 balls of iron of radius 2 cm
= 4*(704/21)= (2816/21)cubic cm
If a larger ball is formed its volume is (2816/21).
If its radius is r,
then (4/3)*(22/7)*(r^3)= (2816/21)
or, r^3= 32
so, r= cubic root of 32 = 3.17, which is less than 4 cm..... Option 5)

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alok   13 years AGO

Volume of 1 ball of iron of radius 2 cm
= (4/3)*(22/7)*(2^3)= (704/21)cubic cm
So, volume of 4 balls of iron of radius 2 cm
= 4*(704/21)= (2816/21)cubic cm
If a larger ball is formed its volume is (2816/21).
If its radius is r,
then (4/3)*(22/7)*(r^3)= (2816/21)
or, r^3= 32
so, r= cubic root of 32 = 3.17, which is less than 4 cm..... Option 5)

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karthikeyan.a   13 years AGO

less than 4 cm

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PADMASHREE   13 years AGO

cube root of 42, appox. less than 4 cube, therefore option is 5

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Achelal Sharma   13 years AGO

the (32)^1/3 = > 3.17

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