Question

1. which will hold more cake batter, the rectangular pan or two round pans? explain your reasoning to a classmate. 2 in. 13 in. 9 in. 2 in. 8 in.

Explanation:

Step1: Calculate the volume of the rectangular pan

The volume formula for a rectangular prism is \(V = l\times w\times h\). Here, \(l = 13\) in, \(w=9\) in, \(h = 2\) in.

$$V_{rectangular}=13\times9\times2=234\space in^{3}$$

Step2: Calculate the volume of one round pan

The volume formula for a cylinder is \(V=\pi r^{2}h\). Given \(d = 8\) in (so \(r=\frac{d}{2}=4\) in) and \(h = 2\) in.

$$V_{one - round}=\pi\times(4)^{2}\times2=\pi\times16\times 2=32\pi\space in^{3}\approx32\times3.14 = 100.48\space in^{3}$$

Step3: Calculate the volume of two round pans

$$V_{two - round}=2\times V_{one - round}=2\times100.48 = 200.96\space in^{3}$$

Answer:

The rectangular pan holds more cake - batter. Since \(V_{rectangular}=234\space in^{3}\) and \(V_{two - round}\approx200.96\space in^{3}\), and \(234>200.96\)