Question

A balloon in the form of a sphere is being filled with a gas. The surface area of the balloonis increasing at the rate of 44%. The volume of the balloon is increasing at the rate of​

Answer 1

Answer:

complete the question

Answer 2

Answer:

The volume of the balloon is increasing at the rate of​ 66%.

Step-by-step explanation:

Assumption,

Let the surface area of the ballon and volume of the ballon of radius 'r' be 'S' and 'V' respectively.

Given,

The rate of change in surface area of ballon is 44%

i.e. ΔS/S × 100 = 44%

Where ΔS = change in surface area.

To find,

The rate of change of volume of the ballon

i.e. ΔV/V × 100

Calculation,

We know that the surface area of the ballon is given by:

S = 4πr²

⇒ ΔS/S × 100 = 2 × Δr/r × 100

⇒ 44% = 2 × Δr/r × 100

⇒ change in percentage of 'r' is 22%.

And, the volume of the sphere is :

V = 4/3 πr³

⇒ ΔV/V × 100 = 3 × Δr/r × 100V

⇒ ΔV/V × 100 = 3 × 22%

⇒  ΔV/V × 100 = 66%

Therefore, the volume of the balloon is increasing at the rate of​ 66%.

#SPJ2