When baking a cake, you have a choice of the following pans:
-a round cake pan that is 2 inches deep and has a 7 inch diameter.
-a 6 inch * 9 inch rectangular pan that is 2 inches deep.
Which of these pans has the larger volume? Justify your answer.
Area of a circle = pi * radius squared
A = pi * r*2
Area of a rectangle = length times width
A = LW
Sorry -- I messed up. I should have given the volume formulas.
Multiply each of the areas by the depth of the pans.
Thank you Ms. Sue
You're welcome.
To determine which pan has the larger volume, we need to calculate the volume of each pan individually. The formula for calculating the volume of a cylinder (the round cake pan) is V = πr^2h, where V is the volume, π is a mathematical constant (approximately equal to 3.14), r is the radius of the circular base, and h is the height of the cylinder.
For the round cake pan:
Radius (r) = Diameter / 2 = 7 inches / 2 = 3.5 inches
Height (h) = 2 inches
Volume of the round cake pan = π * (3.5 inches)^2 * 2 inches
Similarly, the formula to calculate the volume of a rectangular prism (the rectangular pan) is V = lwh, where V is the volume, l is the length of the rectangle, w is the width, and h is the height.
For the rectangular pan:
Length (l) = 9 inches
Width (w) = 6 inches
Height (h) = 2 inches
Volume of the rectangular pan = 9 inches * 6 inches * 2 inches
Now we can compare the two volumes to determine which pan has a larger volume. Simply calculate the value of both formulas and compare the results.
After substituting all the values into the formulas, calculating the volume of the round cake pan gives us approximately 77 cubic inches, while the volume of the rectangular pan is approximately 108 cubic inches.
Based on these calculations, the rectangular pan has a larger volume (108 cubic inches) compared to the round cake pan (77 cubic inches). Therefore, if you are aiming for a larger cake, you should choose the rectangular pan for baking.