Question

V is directly proportional to the cube of (r + 1).
When r = 1, V = 24.
Work out the value of V when r = 2.

Answer 1

Answer:

Step-by-step explanation:

solution

v ∞ $(r + 1)^{3}$

⇒ v = k$(r + 1)^{3}$

    24 = k $(1 + 1)x^{3}$

    24 = k$2^{3}$

    24 = 8k

   ⇒ k = 24/8

        k = 3

there fore when r =2

       ⇒ v = k$(r + 1)^{3}$

      ⇒ v = 3 x $(2 + 1)^{3}$

      ⇒ v = 3 x $3^{3}$

      ⇒ v = 3 x 27

      ⇒ v = 81

Answer 2

Answer:

81

Step-by-step explanation:

Here, V ∝ (r + 1)³, if all conditions remain same and V depends on (r + 1)³ only. Introduce a constant.

V = k(r + 1)³   ⇒ V/(r + 1)³ = k

When r = 1, V = 24:

⇒ k = 24/(1 + 1)³ = 24/2³

      = 24/8 = 3

Hence,

When, r = 2.

⇒ k = V/(r + 1)³

⇒ 3 = V/(2 + 1)³

⇒ 3*(3)³ = V

⇒ 3*27 = V

⇒ 81 = V