Question

spear and cuboid have the same area so that the ratio of volume of a sphere to death the cube is 6 root ratio root Pi

Answer 1

the ratio of volume is us 6/6

Answer 2

Answer:

Step-by-step explanation:

Given---> Sphere and cube have the same area

To show---> Ratio of volume of sphere and volume of cube

Solution---> We know that ,

1) Surface area of sphere = 4 π r²

2) Surface area of cube = 6 a²

3) Volume of sphere = ( 4/3 ) π r³

4) Volume of cube = a³

Let radius of sphere and side of cube be r and x respectively.

ATQ,

Surface area of sphere = Surface area of cube

=> 4 π r² = 6 x²

=> r² / x² = 6 / 4π

=> r² / x² = 3 / 2π

=> r / x = √( 3 / 2π )

Volume of sphere( V₁ ) = ( 4 / 3 ) π r³

Volume of cube ( V₂ ) = x³

V₁ / V₂ = ( 4 / 3 ) π r³ / x³

= ( 4π / 3 ) ( r³ / x³ )

= ( 4π / 3 ) ( r / x )³

= ( 4π / 3 ) { √(3 / 2π ) }³

= ( 4π / 3 ) {√( 3/2π ) }² √( 3/2π )

= ( 4π / 3 ) ( 3 / 2π ) √(3/2π)

= 2 √(3/2π)

= √( 4 × 3 / 2 π )

= √( 2 × 3 / π )

V₁ / V₂ = √6 / √π

=> V₁ : V₂ = √6 : √π