Answer:
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
