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A soup manufacturer sells its soup in right cylindrical cans. The cans have a diameter of 6 centimeters (cm) and a height of 10cm. If the manufacturer fills each can to 90% capacity with soup, what is the volume of soup in each can rounded to the nearest cubic centimeter?

A soup manufacturer sells its soup in right cylindrical cans. The cans have a diameter of 66 centimeters (cm) (\mathrm{cm}) and a height of 10 cm 10 \mathrm{~cm} . If the manufacturer fills each can to 90% 90 \% capacity with soup, what is the volume of soup in each can rounded to the nearest cubic centimeter?

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Q. A soup manufacturer sells its soup in right cylindrical cans. The cans have a diameter of 66 centimeters (cm) (\mathrm{cm}) and a height of 10 cm 10 \mathrm{~cm} . If the manufacturer fills each can to 90% 90 \% capacity with soup, what is the volume of soup in each can rounded to the nearest cubic centimeter?
  1. Calculate total volume of cylindrical can: First, we need to calculate the total volume of the cylindrical can. The formula for the volume of a cylinder is V=πr2hV = \pi r^2 h, where rr is the radius and hh is the height.\newlineGiven the diameter of the can is 6 cm6 \, \text{cm}, the radius rr is half of that, which is 3 cm3 \, \text{cm}. The height hh is given as 10 cm10 \, \text{cm}.\newlineNow we calculate the volume: \newlineV=π×(3 cm)2×10 cmV = \pi \times (3 \, \text{cm})^2 \times 10 \, \text{cm}
  2. Perform volume calculation: Perform the calculation for the volume: \newlineV=π×9 cm2×10 cm=90π cm3V = \pi \times 9 \text{ cm}^2 \times 10 \text{ cm} = 90\pi \text{ cm}^3 \newlineSince π\pi is approximately 3.141593.14159, we can calculate the volume as: \newlineV≈90×3.14159 cm3V \approx 90 \times 3.14159 \text{ cm}^3.
  3. Calculate 9090% of total volume: Now we have the total volume of the can: \newlineV≈282.74 cm3V \approx 282.74\,\text{cm}^3 (rounded to two decimal places for intermediate calculation).\newlineNext, we need to calculate 9090% of this volume to find out how much soup the manufacturer fills in each can.\newline9090% of the total volume is 0.9×282.74 cm30.9 \times 282.74\,\text{cm}^3.
  4. Round to nearest cubic centimeter: Perform the calculation for 9090% of the volume: \newline0.9×282.74 cm3≈254.47 cm30.9 \times 282.74 \, \text{cm}^3 \approx 254.47 \, \text{cm}^3 \newlineWe need to round this to the nearest cubic centimeter.
  5. Final volume of soup in each can: Rounding 254.47 cm3254.47 \, \text{cm}^3 to the nearest cubic centimeter gives us 254 cm3254 \, \text{cm}^3. This is the volume of soup in each can when filled to 90%90\% capacity.

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