How many balls of radius 3cm can be made by melting a bigger ball of diameter 48cm?
- A1024
- B512
- C64
- D256
Solution & Step-by-step Explanation
Given:
Radius of small ball (r) =3cm
Diameter of big ball =48cm⟹ Radius of big ball (R) =
2
48
=24cm
When a solid is melted down to form smaller solid objects, the total volume remains constant.
Volume of big ball=n×Volume of small ball
3
4
πR
3
=n×
3
4
πr
3
Cancelling out
3
4
π from both sides:
R
3
=n×r
3
24
3
=n×3
3
n=(
3
24
)
3
n=8
3
=512
Thus, 512 small balls can be made.
Radius of small ball (r) =3cm
Diameter of big ball =48cm⟹ Radius of big ball (R) =
2
48
=24cm
When a solid is melted down to form smaller solid objects, the total volume remains constant.
Volume of big ball=n×Volume of small ball
3
4
πR
3
=n×
3
4
πr
3
Cancelling out
3
4
π from both sides:
R
3
=n×r
3
24
3
=n×3
3
n=(
3
24
)
3
n=8
3
=512
Thus, 512 small balls can be made.