Question

27 solid iron spheres each of radius 7 cm are melted to form a new sphere find the surface area and volume of new sphere

Answer 1

$\large \tt AHOY!! \:$

ATQ, 27 solid iron spheres each of radius 7 cm are melted to form a new sphere. we have to find the surface area and volume of the new sphere.

volume of the sphere of radius 7cm = 4/3πr³

= 4/3 × 22/7 × 7 × 7 × 7

= 88/3 × 7 × 7

= 4312/3cm³

therefore total volume of 27 such spheres = 4312/3 × 27

= 116424/3

= 38808cm³

hence, the volume of the new sphere is 38808cm³

to find it's radius,

=> 4/3πr³ = 38808cm³

=> 4/3 × 22/7 × r³ = 38808cm³

=> 88/21 × r³ = 38808cm³

=> r³ = 38808/1 × 21/88

=> r³ = 441 × 21

=> r³ = 9261

=> r = ³√9261

=> r = ³√(21 × 21 × 21)

=> r = 21cm

now, TSA (total surface area) of the sphere = 4πr²

= 4 × 22/7 × 21 × 21

= 88 × 3 × 21

= 5544cm²

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