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a spherical balloon is inflated at a rate of 50 m2/min. find the rate at which the radius of the balloon is increasing when the diameter is 20 m.

Respuesta :

The radius of the balloon is increasing at a rate of (5/8π)  when the diameter is 20 m.

What are angles? What is a mathematical function, equation and expression?

  • function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
  • expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.
  • equation : A mathematical equation is used to equate two expressions.

Given is a spherical balloon is inflated at a rate of 50 m²/min.

The surface area of the spherical balloon will be -

S = 4πr²

Now, we can write -

dS/dt = d/dt(4πr²)

dS/dt = 4π x 2r x dr/dt

4π x 2r x dr/dt = 50

dr/dt = (50/8πr)

dr/dt = (100/8πd)

{dr/dt} (d = 20 m) = (5/8π)

Therefore, the radius of the balloon is increasing at a rate of (5/8π)  when the diameter is 20 m.

To solve more questions on functions, expressions and polynomials, visit the link below -

brainly.com/question/17421223

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