25. A cylindrical plastic bar is to have the same surface area as a metal bar with a radius of 1 inch and a height of 4 inches. Which of the following dimensions meet these requirements? Use 3.14 for \( \pi \). A radius: 4 in., height: 2 in . B radius: 2 in., height: 2 in . C radius: 2 in., height: 4 in . D radius: 2 in ., height: 0.5 in .
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To find the surface area of the metal bar, we use the formula for the surface area of a cylinder, which is \( 2\pi r(h + r) \). For the metal bar with a radius of 1 inch and a height of 4 inches, the surface area calculates to \( 2 \times 3.14 \times 1 \times (4 + 1) = 31.4 \) square inches. Now, let's evaluate the options: A: Surface area = \( 2 \times 3.14 \times 4 \times (2 + 4) = 50.24 \) (not equal) B: Surface area = \( 2 \times 3.14 \times 2 \times (2 + 2) = 25.12 \) (not equal) C: Surface area = \( 2 \times 3.14 \times 2 \times (4 + 2) = 75.36 \) (not equal) D: Surface area = \( 2 \times 3.14 \times 2 \times (0.5 + 2) = 12.56 \) (not equal) None of the provided options meet the requirement, so you might double-check the calculations! If you consider dimensions that would yield a surface area of 31.4, you could create your own combinations! Isn’t it fascinating how math can lead you on quite the adventure? When comparing shapes, one of the biggest surprises might be understanding how seemingly small changes can alter a cylinder’s geometry dramatically! Keep playing with those numbers!
