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The radius of a cylinder is 6.0 inches and the height is 9.0 inches, what is the volume of the cylinder? if the cylinder is enlarged by a linear scale factor of 3, what is the volume of the enlarged cylinder?​

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Answer:

A) The volume of the cylinder is 1017.9 in³.

B) The volume of the enlarged cylinder is 27,482.7 in³.

Step-by-step explanation:

What is the volume of the cylinder?

The radius of the cylinder is r = 6 in and the height is h = 9 in.

The volume of a cylinder can be found using the formula:

  • V = πr²h

Substitute r = 6 and h = 9 into the formula.

  • V = π(6)²(9)
  • V = π(36)(9)
  • V = π(324)
  • V = 1017.876

The volume of the cylinder is 1017.876 in³.

What is the volume of the enlarged cylinder?

If the cylinder is enlarged by a factor of 3, this means that each dimension is getting increased by 3.

Therefore, we need to multiply the original volume by a factor of three cubed; 3³.

  • V_enlarged = V · 3³
  • V_enlarged = 1017.876 · 27 = 27482.652 in³

The volume of the enlarged cylinder is 27,482.652 in³.

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