Three spherical metal balls of radii 6cm,8cm and R cm are melted into a solid sphere of radius 12cm. The value

Question

of R
choice

a) 5cm
b) 6cm
c) 8cm
d) 10cm

Answer 1

d) 10 cm

Just work out the volume of each sphere......
using-: Volume = 4/3 * pi * r^3

Then add together the volumes of the 6cm and 8cm spheres and subtract this value from the 12cm Volume sphere.

Now take the cube root of this figure (which is 1000) and I guarantee you will get 10cm.

Answer 2

Volume of large sphere = sum of volumes of small spheres.

As volume is proportional to cube of radius,

6^3 + 8^3 + R^3 = 12^3

which gives R = 10 cm.

Answer 3

4/3 pi.r^3 is the volume of a sphere of radius r.

We take 4/3 as 1.333 for simplicity sake and pi as 3.14

So we have

1.333 x 3.14 x 12^3 = 1.333 x 3.14 x 6^3 + 1.333 x 3.14 x 8^3 + 1.333 x 3.14 x R^3

Since 1.333 and 3.14 are common, we can remove them.

So, we have

12^3 = 6^3 + 8^3 + R^3

1728 = 216 + 512 + R^3

R^3 = 1728 - 728 = 1000

So, R = Cubic root of 1000 = 10

R = 10 cm is the answer.

Answer 4

The value will be as calculated below.
Sum of volume of three balls =volume of new ball formed
6^3+8^3+r^3=12^3
r^3=1000 =10^3
so, r=10 cm.

Answer 5

This is how you solve it :
Volume of Big Metal Ball = Sum of Volume of smalled balls.
4/3*3.14*12^3=4/3*3.14*R^3+4/3*3.14*6^3+4/3*3.14*8^3, Just remove the 4/3*3.14 which is Constant.
12^3=R^3+6^3+8^3
1728=R^3+216+512
R^3=1728-(216+512)
R^3=1728-728
R^3=1000
R=10
The answer is D.

Answer 6

10cm
because 6^3+8^3+10^3=12^3

Answer 7

the vol. of final sphere should be equal to the sum of volumes of other three spheres


[(4/3)*(22/7)*{6^3+8^3+R^3}] = [(4/3)*(22/7)*{12^3}]

6^3+8^3+R^3 = 12^3

Answer 8

Volume of sphere = 4/3 pi r3

6CM VOL = 288 pi

8CM VOL = 682.666... pi

12cm VOL = 2304 pi

So the volume of the other sphere =

2304 - (682.66666...+ 288)

= 1333.333... pi

R= 3/4 VOL CUBE ROOT

= 10cm

So the answer is d) = 10

Answer 9

answer d) 10 cm radius

6^3 + 8^3 + R^3 = 12^3
R^3 = 1000
R = 10 cm

Answer 10

(12^3 - 6^3 - 8^3)^(1/3) = 10 cm