Question

Robert sketches two rectangular prisms, A and B. Prism A's side lengths are 5 centimeters, 6 centimeters, and 7 centimeters. Prism B's side lengths were twice those of prism A's: 10 centimeters, 12 centimeters, and 14 centimeters. Robert says the surface area of prism B is twice the surface area of prism A. Is he correct? If he is not, how many times as great as prism A's surface area is prism B's surface area? Show your work.​

Answer 1

• Robert is wrong, the correct answer is 4 times greater

Explanation:

Area is the product of two dimensions.

If each dimension is doubled, then the area becomes 2*2 = 4 times greater.

If each face is 4 times greater, then their sum will be 4 times greater.

The sum of the faces is the total surface area, therefore the B's surface area is 4 times as great as A's surface area.