Question

If V ∝ r³ and V=36π when r=3 then relation between V and r is___
a. V=πr³
b. V= ⅓πr³
c. V=⅔πr³
d. V=4/3πr³

plz show me the whole method​

Answer 1

Given:-

→ V ∝ r³

→ V = 36π, when r = 3

To find:-

→ Relation between V and r .

Solution:-

=> V = 36π ----(1)

=> r = 3

Since, we have v ∝ r³, so by cubing both sides in the equation r = 3, we get :-

=> (r)³ = (3)³

=> r³ = 27 ----(2)

Now, on dividing eq.1 by eq.2, we get :-

=> V/r³ = 36π/27

=> V/r³ = 4π/3

=> V = 4π/3 × r³

=> V = 4/3πr³

Thus, relation between V and r is

V = 4/3πr³ [ Option. d ]

Verification:-

To verify our answer let's take 36π(V) in the L.H.S and let's solve the R.H.S :-

=> V = 4/3πr³

=> 36π = 4/3 × π × 3 × 3 × 3

=> 36π = 4 × π × 9

=> 36π = 36π

Hence, LHS = RHS verified !!!

Answer 2

Given:-

→ V ∝ r³

→ V = 36π, when r = 3

To find:-

→ Relation between V and r .

Solution:-

=> V = 36π ----(1)

=> r = 3

Since, we have v ∝ r³, so by cubing both sides in the equation r = 3, we get :-

=> (r)³ = (3)³

=> r³ = 27 ----(2)

Now, on dividing eq.1 by eq.2, we get :-

=> V/r³ = 36π/27

=> V/r³ = 4π/3

=> V = 4π/3 × r³

=> V = 4/3πr³

Thus, relation between V and r is

V = 4/3πr³ [ Option. d ]

Verification:-

To verify our answer let's take 36π(V) in the L.H.S and let's solve the R.H.S :-

=> V = 4/3πr³

=> 36π = 4/3 × π × 3 × 3 × 3

=> 36π = 4 × π × 9

=> 36π = 36π

Hence, LHS = RHS verified !!!