Question

PLEASE HELP!!! When baking a cake you can choose between a round pan with a 12 in. diameter and a 8 in.×11 in. rectangular pan. ​ a) Determine the area of the base of each pan. ​b) If both pans are 2 in.​ deep, determine the volume of each pan. ​c) Which pan has the larger​ volume?

Answer 1

The area of the round pan is 36π square inches, and the rectangular pan is 88 square inches. The volume of the round pan is 72π cubic inches, and the rectangular pan is 176 cubic inches. The rectangular pan has the larger volume.

Step-by-step explanation:

To answer the student's question regarding the area and volume of different pans, first, let's calculate the area of each pan:

Area of the round pan: Since the diameter is 12 inches, the radius (r) is half of that, which is 6 inches. The formula for the area (A) of a circle is A = πr². So, the area of the round pan is π(6²) = 36π square inches.

Area of the rectangular pan: The formula for the area of a rectangle is A = length × width. Therefore, the area of the 8 in. × 11 in. rectangular pan is 8 × 11 = 88 square inches.

Next, we'll calculate the volume for each pan, given they are both 2 inches deep:

Volume of the round pan: The volume (V) of a cylinder (round pan is a cylinder shape) is V = base area × height. Thus, the volume of the round pan is 36π × 2 = 72π cubic inches.

Volume of the rectangular pan: The volume of a rectangular prism (the shape of the rectangular pan) is V = base area × height. Hence, the volume of the rectangular pan is 88 × 2 = 176 cubic inches.

Comparing the volumes, the rectangular pan has a larger volume of 176 cubic inches, contrasting with the round pan's volume of 72π, which is approximately 226.19 cubic inches.

One helpful tip for remembering geometric formulas is dimensional analysis—ensuring units are consistent—and using familiar shapes such as squares and rectangles to simplify the understanding of areas and volumes.

Answer 2

A) to work out area of a circular pan you use 3.14 x R^2 so the area would be 3.14x(6)^2, which gives us 113.04in^2. The rectangular pan has area 8x11 which is 88in^2.
B) to work out volume you multiple the areas by the depth. So the circular one is 226.09in^3 and the rectangular one is 176in^3.
C) this means that the circular pan has a larger volume
Hope this helped and sorry if anything is wrong :)