Question

prism a and prism b are rectangular prisms.
. prism a is 3 inches by 2 inches by 1 inch.
. prism b is 1 inch by 1 inch by 6 inches.

select all statements that are true about the two prisms.
a they have the same volume.
b they have the same number of faces.
c more inch - cubes can be packed into prism a than into prism b.
d the two prisms have the same surface area.
e the surface area of prism b is greater than that of prism a.

Explanation:

Step1: Calculate volume of Prism A

The volume formula for a rectangular - prism is $V = l\times w\times h$. For Prism A with $l = 3$ inches, $w = 2$ inches and $h = 1$ inch, $V_A=3\times2\times1 = 6$ cubic inches.

Step2: Calculate volume of Prism B

For Prism B with $l = 1$ inch, $w = 1$ inch and $h = 6$ inches, $V_B=1\times1\times6 = 6$ cubic inches. So, they have the same volume.

Step3: Consider number of faces

Both rectangular prisms have 6 faces.

Step4: Analyze surface - area

The surface - area formula for a rectangular prism is $SA=2(lw + lh+wh)$.
For Prism A: $SA_A = 2(3\times2+3\times1 + 2\times1)=2(6 + 3+2)=2\times11 = 22$ square inches.
For Prism B: $SA_B=2(1\times1+1\times6+1\times6)=2(1 + 6+6)=2\times13 = 26$ square inches. So, the surface - area of Prism B is greater than that of Prism A.

Answer:

A. They have the same volume.
B. They have the same number of faces.
E. The surface area of Prism B is greater than that of Prism A.