Question

containers a and b hold oatmeal. container a is a rectangular prism and container b is a cylinder. which has a larger volume: container a or b? container a container b explain your thinking.

Explanation:

Step1: Calculate Volume of Container A (Rectangular Prism)

The formula for the volume of a rectangular prism is \( V = l \times w \times h \). For Container A, \( l = 10 \) in, \( w = 4 \) in, \( h = 6 \) in. So, \( V_A = 10 \times 4 \times 6 \).
\( V_A = 240 \) cubic inches.

Step2: Calculate Volume of Container B (Cylinder)

The formula for the volume of a cylinder is \( V = \pi r^2 h \). The diameter of Container B is 5 in, so radius \( r = \frac{5}{2} = 2.5 \) in, and height \( h = 10 \) in. Then, \( V_B = \pi \times (2.5)^2 \times 10 \).
\( V_B = \pi \times 6.25 \times 10 = 62.5\pi \approx 62.5 \times 3.14 = 196.25 \) cubic inches.

Step3: Compare Volumes

Compare \( V_A = 240 \) and \( V_B \approx 196.25 \). Since \( 240 > 196.25 \), Container A has a larger volume.

Answer:

Container A