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A cake pan is in the shape of a right rectangular prism 20 centimeters (cm) long by 20cm wide by 5cm high. The pan contains 1,000 cubic centimeters (cm^(3)) of batter. Approximately how far is the cake batter from the top of the pan? Choose 1 answer: (A) 1cm (B) 2.5cm (C) 5cm (D) 7cm

A cake pan is in the shape of a right rectangular prism 20 cm20\,\text{cm} long by 20 cm20\,\text{cm} wide by 5 cm5\,\text{cm} high. The pan contains 1,000 cm31,000\,\text{cm}^3 of batter. Approximately how far is the cake batter from the top of the pan?\newline Choose 11 answer:\newline (A) 1 cm1\,\text{cm}\newline (B) 2.5 cm2.5\,\text{cm}\newline (C) 5 cm5\,\text{cm}\newline (D) 7 cm7\,\text{cm}

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Q. A cake pan is in the shape of a right rectangular prism 20 cm20\,\text{cm} long by 20 cm20\,\text{cm} wide by 5 cm5\,\text{cm} high. The pan contains 1,000 cm31,000\,\text{cm}^3 of batter. Approximately how far is the cake batter from the top of the pan?\newline Choose 11 answer:\newline (A) 1 cm1\,\text{cm}\newline (B) 2.5 cm2.5\,\text{cm}\newline (C) 5 cm5\,\text{cm}\newline (D) 7 cm7\,\text{cm}
  1. Calculate Pan Volume: Calculate the volume of the cake pan.\newlineVolume of the pan = Length×Width×Height\text{Length} \times \text{Width} \times \text{Height}\newlineVolume of the pan = 20 cm×20 cm×5 cm20 \, \text{cm} \times 20 \, \text{cm} \times 5 \, \text{cm}\newlineVolume of the pan = 20002000 cubic centimeters
  2. Determine Batter Volume: Determine the volume of the cake batter already in the pan. Volume of the batter = 10001000 cubic centimeters
  3. Calculate Remaining Volume: Calculate the remaining volume in the pan that is not occupied by the batter.\newlineRemaining volume = Volume of the pan - Volume of the batter\newlineRemaining volume = 20002000 cubic centimeters - 10001000 cubic centimeters\newlineRemaining volume = 10001000 cubic centimeters
  4. Calculate Remaining Height: Calculate the height that the remaining volume would occupy.\newlineSince the length and width of the pan are unchanged, the remaining volume will occupy a height in the pan that can be calculated by dividing the remaining volume by the area of the base of the pan.\newlineHeight of remaining volume = Remaining volume / (Length ×\times Width)\newlineHeight of remaining volume = 10001000 cubic centimeters / (2020 cm ×\times 2020 cm)\newlineHeight of remaining volume = 10001000 cubic centimeters / 400400 square centimeters\newlineHeight of remaining volume = 2.52.5 centimeters

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