A spherical ball of lead 5 cm in diameter is melted and recast into three spherical balls. The diameters of the two of these balls are 2cm and 2(14.5)^⅓ cm. Find the diameter of the third ball.
Answers
Answer:
Radius of first spherical ball = \cfrac {2}{2} = 1 cm=
2
2
=1 cm
Radius of second spherical ball = \cfrac {2 \sqrt [3] {14.5}}{2} = \sqrt [3] {14.5} cm=
2
2
3
14.5
=
3
14.5
cm
Let the radius of the third ball be rr cm.
Radius of the main spherical ball = \cfrac {5}{2} cm = 2.5 cm=
2
5
cm =2.5 cm
Volume of main spherical bead == Volume of spherical bead 1 +1+Volume of spherical bead 2 +2+ Volume of spherical bead 33
Volume of a sphere = \cfrac { 4 }{ 3 } \pi { r }^{ 3 }=
3
4
πr
3
So, \cfrac { 4 }{ 3 } \pi \times { 2.5 }^{ 3 } = \cfrac { 4 }{ 3 } \pi { 1 }^{ 3 } + \cfrac { 4 }{ 3 } \pi { (\sqrt [3] {14.5}) }^{ 3 } + \cfrac { 4 }{ 3 } \pi { r }^{ 3 }
3
4
π×2.5
3
=
3
4
π1
3
+
4
3π(
3
14.5
)
3
+
3
4
πr
3
\Rightarrow { 2.5 }^{ 3 } = { 1 }^{ 3 } + { (\sqrt [3] {14.5}) }^{ 3 } + { r }^{ 3 }⇒ 2.5
3
=1
3
+(
3
14.5
)
3
+r
3
\Rightarrow { r }^{ 3 } = 15.625 - 1 - 14.5⇒r
3
=15.625−1−14.5
\Rightarrow { r }^{ 3 } = 0.125 = 0.5 \times 0.5 \times 0.5 ⇒r
3
=0.125=0.5×0.5×0.5
\Rightarrow r = 0.5 cm ⇒r =0.5 cm
Hence, the diameter of the third spherical bead is 2 \times 0.5 = 1 cm2×0.5=1 cm.
Step-by-step explanation: