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Difficulty: EasyVolume and Surface Area of Solids

A right circular cylinder has a volume of 20 cubic inches20\text{ cubic inches}. If the radius of the cylinder is tripled and its height remains the same, what is the volume, in cubic inches, of the new cylinder?

  1. A
    60
  2. B
    120
  3. 180Answer
  4. D
    540

Answer

180
The volume of a right circular cylinder is calculated using the formula V=πr2hV = \pi r^2 h. When the radius rr is tripled to 3r3r and the height hh remains constant, the volume is multiplied by 32=93^2 = 9. Thus, the new volume is 99 times the original volume of 2020 cubic inches, which equals 180180 cubic inches.

Step-by-Step Solution

1
Write down the formula for the volume of a right circular cylinder.
V=πr2hV = \pi r^2 h
To identify how the volume of a cylinder relates to its radius and height.
2
Determine the effect of tripling the radius on the volume formula.
Vnew=π(3r)2h=9πr2hV_{\text{new}} = \pi (3r)^2 h = 9\pi r^2 h
Substituting the new radius 3r3r into the formula shows that the new volume is 9 times the original volume.
3
Substitute the original volume of 2020 cubic inches into the expression for the new volume.
Vnew=9×20=180V_{\text{new}} = 9 \times 20 = 180
Since the original volume πr2h\pi r^2 h equals 2020, we multiply this value by 9 to find the new volume.

Key Concept

Volume of a cylinder and dimensional scaling
Estimated Time:45s
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Topics

Volume and Surface Area of Solids

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