when making a cake you have a choice of the following pants
a round cake pan that is 2 inches deep and has a 7-inch diameter or a 6-inch x 9-inch rectangular cake pan that is 2-in deep
which of these pans has the larger volume justify your answer
Come on bot, it's basic arithmetic
volume of round cake = PÏ€(3.5)^2 (2) = 76.97 in^3
volume of rectangular cake = (6)(9)(2) in^3 = 108 in^3
obviously the round cake is the smaller of the two
To determine which pan has the larger volume, we need to calculate the volume of each pan.
For the round cake pan, we can use the formula for the volume of a cylinder, which is given by:
Volume = π * r^2 * h
where π is a constant (approximately 3.14159), r is the radius of the circular base (half the diameter), and h is the height or depth.
In this case, the round cake pan has a 7-inch diameter, so the radius (r) would be 7/2 = 3.5 inches. The height or depth (h) is given as 2 inches.
So, the volume of the round cake pan would be:
Volume = π * (3.5)^2 * 2
For the rectangular cake pan, we can use the formula for the volume of a rectangular prism, which is given by:
Volume = l * w * h
where l is the length, w is the width, and h is the height or depth.
In this case, the rectangular cake pan has dimensions of 6 inches by 9 inches, with a depth of 2 inches.
So, the volume of the rectangular cake pan would be:
Volume = 6 * 9 * 2
Now, we can calculate the volumes of both pans to determine which one is larger.
Volume of round cake pan = π * (3.5)^2 * 2
Volume of rectangular cake pan = 6 * 9 * 2
Using a calculator, we can compute the values.
Volume of round cake pan ≈ 3.14159 * 3.5^2 * 2 ≈ 77.95 cubic inches
Volume of rectangular cake pan = 6 * 9 * 2 = 108 cubic inches
Comparing the volumes, we can see that the rectangular cake pan has a larger volume (108 cubic inches) than the round cake pan (approximately 77.95 cubic inches). Therefore, the rectangular cake pan has the larger volume.
To determine which pan has a larger volume, we need to calculate the volume of each pan by using the formula for the volume of a cylinder (for the round pan) and the formula for the volume of a rectangular prism (for the rectangular pan).
1. Round cake pan:
The volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height (or depth in this case).
Given that the round cake pan has a diameter of 7 inches, the radius (r) is half of the diameter, which is 7/2 = 3.5 inches.
The height (h) of the round cake pan is given as 2 inches.
Using the formula V = πr^2h, we can calculate the volume of the round pan:
V = π(3.5)^2(2) = 38.5π cubic inches
2. Rectangular cake pan:
The volume of a rectangular prism can be calculated using the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height (or depth in this case).
Given that the rectangular cake pan has dimensions of 6 inches by 9 inches, we have:
Length (l) = 9 inches
Width (w) = 6 inches
Height (h) = 2 inches
Using the formula V = lwh, we can calculate the volume of the rectangular pan:
V = (9)(6)(2) = 108 cubic inches
Now we can compare the volumes:
The round pan has a volume of 38.5Ï€ cubic inches, which is approximately 120.74 cubic inches.
The rectangular pan has a volume of 108 cubic inches.
Therefore, the rectangular cake pan has a larger volume than the round cake pan.