Question

Pairs of radii 3 cm 4 cm and 5 cm are melted together to form a single sphere find the radius of the sphere

Answer 1

$\large \tt AHOY!! \:$


ATQ, spheres of radii 3 cm 4 cm and 5 cm are melted together to form a single sphere. we have to find the radius of new sphere formed.

total volume of the three spheres of radius 3cm, 4cm and 5cm = volume of the new sphere

volume of the sphere of radius 3cm = 4/3πr³

= 4/3 × 22/7 × 3 × 3 × 3

= 88/21 × 3 × 3 × 3

= 2376/21cm³

volume of the sphere of radius 4cm = 4/3πr³

= 4/3 × 22/7 × 4 × 4 × 4

= 88/21 × 4 × 4 × 4

= 5632/21cm³

volume of the sphere of radius 5cm = 4/3πr³

= 4/3 × 22/7 × 5 × 5 × 5

= 88/21 × 5 × 5 × 5

= 11000/21cm³

therefore total volume = 2376/21 + 5632/21 + 11000/21

= (2376 + 5632 + 11000)/21

= 19008/21cm³

therefore the volume of the new sphere is also 190008/21cm³

to find it's radius,

=> 4/3πr³ = 19008/21cm³

=> 4/3 × 22/7 × r³ = 19008/21cm³

=> 88/21 × r³ = 19008/21cm³

=> r³ = 19008/21 × 21/88

=> r³ = 216

=> r = ³√216

=> r = ³√(6 × 6 × 6)

=> r = 6cm

hence, the radius of the single sphere formed is 6cm.

$\large \tt HOPE \: THIS \: HELPS!!$

Answer 2

Step-by-step explanation:

$\bf \underline{Given-}$

Radius of Three Metallic Spheres are 3 cm , 4 cm and 5 cm.

$\bf \underline{To\: find-}$

Radius of New Shape who makes by melting those there sphare

$\bf \underline{Solution-}$

$\textsf{We know that,}$

$\pink{\boxed{\bf{Volume\ of \ Sphare = \dfrac{4}{3}πr³}}}$

$\textsf{Valume of Sphare whose radius is 3.}$

$\small\sf{~~~~~:\implies.Volume= \dfrac{4}{3} \times \dfrac{22}{7} \times 3³}$

$\small\sf{~~~~~:\implies Volume= \dfrac{88}{21} \times 27}$

$\small\sf{~~~~~:\implies Volume= 4.2 \times27}$

$\small\sf{~~~~~:\implies Volume= 112.4}$

$\textsf{Valume of Sphare whose radius is 3= 112.4cm³}$

$\textsf{Valume of Sphare whose radius is 4.}$

$\small \sf{~~~~~:\implies Volume= \dfrac{4}{3} \times \dfrac{22}{7} \times 4³}$

$\small\sf{~~~~~:\implies Volume= \dfrac{88}{21} \times 64}$

$\small\sf{~~~~~:\implies Volume= 4.2\times 64}$

$\small\sf{~~~~~:\implies Volume=268.8}$

$\textsf{Valume of Sphare whose radius is 4=268.8cm³}$

$\textsf{Valume of Sphare whose radius is 5.}$

$\small\sf{~~~~~:\implies Volume= \dfrac{4}{3} \times \dfrac{22}{7} \times 5³}$

$\small\sf{~~~~~:\implies Volume= \dfrac{88}{21} \times 125}$

$\small\sf{~~~~~:\implies Volume=4.2 \times 125}$

$\small\sf{~~~~~:\implies Volume=525}$

$\textsf{Valume of Sphare whose radius is 5=525cm³}$

$\textsf{Now it is Given that All 3 Sphare are mealted and convert into a new Sphare}$

$\textsf{Volume of new sphare = 112.4+268.8+225 }$

$\textsf{Volume of new sphare = 906.8}$

$\textsf{Radius of New Sphare = ?}$

$\boxed{\bf{Volume\ of \: new \: Sphare = \dfrac{4}{3}πr³}}$

$\sf{~~~~~:\implies 906.8 = \dfrac{4}{3} \times \dfrac{ 22}{7} \times r³}$

$\sf{ ~~~~~:\implies r³ = \dfrac{906.8 \times 21}{88} }$

$\sf{ ~~~~~:\implies r³ = \dfrac{19030.2}{88} }$

$\sf{~~~~~:\implies r³ = 216 }$

$\sf{ ~~~~~:\implies r = \sqrt[3]{216} }$

$\sf{~~~~~:\implies r = \sqrt[3]{6 \times 6 \times 6} }$

$\sf{ ~~~~~:\implies r = \sqrt[3]{ {6}^{3}} }$

$\sf{ ~~~~~:\implies r = 6 }$

$\bf \underline{Hance,the \:radius\: of \:New\: Sphere\: is\: 6 cm.-}$