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Janine works at a factory and is filling cylindrical molds with molten plastic. It takes 9.6 cubic centimeters of molten plastic to fill the molds to a height of 0.8 centimeters. To the nearest whole centimeter, what is the radius of the cylindrical mold?

Janine works at a factory and is filling cylindrical molds with molten plastic. It takes 99.66 cubic centimeters of molten plastic to fill the molds to a height of 00.88 centimeters. To the nearest whole centimeter, what is the radius of the cylindrical mold?

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Full solution

Q. Janine works at a factory and is filling cylindrical molds with molten plastic. It takes 99.66 cubic centimeters of molten plastic to fill the molds to a height of 00.88 centimeters. To the nearest whole centimeter, what is the radius of the cylindrical mold?
  1. Given Volume and Height: We are given the volume of the cylindrical mold and the height, and we need to find the radius. The formula for the volume of a cylinder is V=πr2hV = \pi r^2 h, where VV is the volume, rr is the radius, and hh is the height.
  2. Volume Formula Calculation: We know the volume VV is 9.69.6 cubic centimeters and the height hh is 0.80.8 centimeters. We can plug these values into the formula and solve for the radius rr.
  3. Calculate r2r^2: The formula with the given values is 9.6=πr2(0.8)9.6 = \pi r^2(0.8). To find r2r^2, we first need to divide both sides of the equation by π\pi and then by the height (0.8)(0.8).
  4. Divide by Height: Dividing 9.69.6 by π\pi (3.143.14) gives us 9.63.14≈3.0573\frac{9.6}{3.14} \approx 3.0573. Now we divide this result by the height (0.80.8) to get r2r^2.
  5. Find r: Dividing 3.05733.0573 by 0.80.8 gives us r2≈3.8216r^2 \approx 3.8216. To find rr, we need to take the square root of both sides.
  6. Final Radius Calculation: The square root of 3.82163.8216 is approximately 1.95491.9549. Since we need to round to the nearest whole centimeter, we round this to 22 centimeters.

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