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A container is an open cylinder whose height and radius are of equal length. The total surface area of the container is 300 cm³. Find the radius of the container.​

Respuesta :

mhanifa

Answer:

  • The radius of the container is approximately 4.89 cm

Step-by-step explanation:

Given

A container with:

  • r = h
  • S = 300 cm²

To find

  • The radius of the container

Solution

Use the equation for total surface area of cylinder:

  • S = 2πr² + 2πrh or S = 2πr(r + h)

Since we have r = h and the value of S is known, let's solve this equation:

  • 2πr(r + h) = 300
  • 2πr(r + r) = 300
  • 2πr(2r) = 300
  • 4πr² = 300
  • πr² = 75
  • 3.14r² = 75
  • r² = 75/3.14
  • r² = 23.89 (rounded)
  • r = √23.89
  • r = 4.89 cm (rounded)

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