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 prisms. 10 points 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. hint: there will be 3 correct answers.

They have the same volume ⇒ A

have the same number of faces ⇒ B

The surface area of Prism B is greater than that of Prism A ⇒ E

Step-by-step explanation:

* Lets revise the volume and the surface area of any rectangular prism

- The volume of a prism = Area of its base × height

  V = length × width × height

- The surface area = perimeter base × height + 2 × area base

   S.A = (2 length + 2 width) × height + 2 (length × width)

- Any rectangular prism has 6 faces, 8 vertices and 12 edges

∵ The dimensions of prism A are 3 inches, by 2 inches, by 1 inch

∵ The dimensions of prism B are 1 inch, by 1 inch, by 6 inches

∴ Volume A = 3 × 2 × 1 = 6 inches³

∴ Volume B = 1 × 1 × 6 = 6 inches³

∴ They have the same volume ⇒ A

∵ S.A of A = [(2)(3) + (2)(2)] × 1 + 2 × 3 × 2 = [6 + 4] × 1 + 12

∴ S.A of A = 10 + 12 = 22 inches²

∵ S.A of B = [(2)(1) + (2)(1)] × 6 + 2 × 1 × 1 = [2 + 2] × 6 + 2

∴ S.A of B = 24 + 2 = 26 inches²

∴ The surface area of Prism B is greater than that of Prism A ⇒ E

∵ Prism A has 6 faces

∵ Prism B has 6 faces

∴ have the same number of faces ⇒ B

* The true statements are:

They have the same volume ⇒ A

have the same number of faces ⇒ B

The surface area of Prism B is greater than that of Prism A ⇒ E

$119.20

step-by-step explanation:

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