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Whitney is making a strawberry cake for her brother's birthday. The cake pan is a right rectangular prism 20cm wide by 28cm long. Whitney puts 1848cm^(3) of batter into the pan. How deep is the cake batter? ◻cm

Whitney is making a strawberry cake for her brother's birthday. The cake pan is a right rectangular prism 20 cm20\,\text{cm} wide by 28 cm28\,\text{cm} long. Whitney puts 1848 cm31848\,\text{cm}^{3} of batter into the pan. \newlineHow deep is the cake batter?\newline□ cm\square\,\text{cm}

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Pythagorean Theorem and its converseright chevron icon

Full solution

Q. Whitney is making a strawberry cake for her brother's birthday. The cake pan is a right rectangular prism 20 cm20\,\text{cm} wide by 28 cm28\,\text{cm} long. Whitney puts 1848 cm31848\,\text{cm}^{3} of batter into the pan. \newlineHow deep is the cake batter?\newline□ cm\square\,\text{cm}
  1. Calculate Volume of Cake Pan: Calculate the volume of the cake pan using the formula for the volume of a rectangular prism: Volume=length×width×height\text{Volume} = \text{length} \times \text{width} \times \text{height}.
  2. Plug in Given Dimensions: Plug in the given dimensions: Volume = 28 cm×20 cm×height.28\,\text{cm} \times 20\,\text{cm} \times \text{height}.
  3. Set Equal to Solve for Height: We know the volume of batter Whitney put into the pan is 1848 cm31848\,\text{cm}^3. Set this equal to the volume of the pan to solve for the height (depth): 28 cm×20 cm×height=1848 cm328\,\text{cm} \times 20\,\text{cm} \times \text{height} = 1848\,\text{cm}^3.
  4. Isolate Height: Divide both sides of the equation by the product of the length and width to isolate the height: height=1848 cm3(28 cm×20 cm)\text{height} = \frac{1848\,\text{cm}^3}{(28\,\text{cm} \times 20\,\text{cm})}.
  5. Calculate Height: Calculate the height: height=1848cm3560cm2\text{height} = \frac{1848\text{cm}^3}{560\text{cm}^2}.
  6. Perform Division: Perform the division: height=3.3 cm.\text{height} = 3.3\,\text{cm}.

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