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 x 9 inch rectangular cake pan that is 2 inches deep
Which of these has the larger volume? Justify your answer.
HELPPPPP!!!!!!
since both have the same height, just compare the areas
compare π*(7/2)^2 and 6*9
To determine which pan has the larger volume, we need to calculate the volume of each pan.
Volume of a round cake pan can be calculated using the formula:
V = π * r^2 * h
where V is the volume, π is a constant (approximately 3.14), r is the radius of the pan, and h is the height (depth) of the pan.
Volume of a rectangular cake pan can be calculated using the formula:
V = l * w * h
where V is the volume, l is the length of the pan, w is the width of the pan, and h is the height (depth) of the pan.
Let's calculate the volume of each pan:
For the round cake pan:
Radius (r) = diameter / 2 = 7 inches / 2 = 3.5 inches
Height (h) = 2 inches
V(round) = π * 3.5^2 * 2
V(round) ≈ 3.14 * 12.25 * 2
V(round) ≈ 77.38 cubic inches
For the rectangular cake pan:
Length (l) = 9 inches
Width (w) = 6 inches
Height (h) = 2 inches
V(rectangular) = 9 * 6 * 2
V(rectangular) = 108 cubic inches
Comparing the volumes, we find that the volume of the rectangular cake pan (V(rectangular) = 108 cubic inches) is larger than the volume of the round cake pan (V(round) ≈ 77.38 cubic inches).
Therefore, the rectangular cake pan has a larger volume.
Hope this helps!
To determine which pan has the larger volume, we need to calculate the volume of each pan. The formula for finding the volume of a rectangular box (such as a cake pan) is V = length x width x height, while the formula for finding the volume of a cylinder (such as a round cake pan) is V = π x radius^2 x height.
Let's start with the round cake pan. The height of the pan is given as 2 inches and the diameter (which is equal to twice the radius) is given as 7 inches. So, the radius of the pan is 7 inches / 2 = 3.5 inches.
Using the formula V = π x radius^2 x height, we can calculate the volume of the round cake pan as:
V = π x (3.5 inches)^2 x 2 inches
V ≈ 3.14 x 12.25 square inches x 2 inches
V ≈ 76.96 cubic inches
Now let's move on to the rectangular cake pan. The height of the pan is again given as 2 inches, and the dimensions are given as 6 inches x 9 inches.
Using the formula V = length x width x height, we can calculate the volume of the rectangular cake pan as:
V = 6 inches x 9 inches x 2 inches
V = 108 cubic inches
Comparing the volumes, we find that the rectangular cake pan has a larger volume of 108 cubic inches, while the round cake pan has a volume of 76.96 cubic inches.
Therefore, the rectangular cake pan has the larger volume.