Question

PLZ HELP!

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?


Robert is 1.___; the Surface area of A is ____ square centimeters. The Surface area of B is _____square centimeters. B's surface area is ____ times as great as A's.

Answer 1

Prism B's surface area is 4 times Prism A's.

The surface area of Prism A is 214 square centimeters.

The surface area of Prism B is 856 square centimeters.

Explanation:

To find the surface area of a rectangular prism, use this formula:

`A=2(wl+hl+hw)`

Where w is the width, h is the height, and l is the length.

Substitute the values given for Prism A and Prism B into the formula to find each prism's surface area:

Prism A:

`A=2(5 * 6+6 * 7+5 * 7)\\A = 2 (30 + 42 + 35)\\A = 214`

Prism B:

`A=2(10*12+12*14+14*10)\\A = 2 (120 + 168 + 140)\\A = 856`

Prism B's surface area is 4 times Prism A's.

The surface area of Prism A is 214 square centimeters.

The surface area of Prism B is 856 square centimeters.

Answer 2

4 times greater

Explanation:

Prism A

SA = 2 (lw+wh+lh) where l is length w is width and h is height

SA = 2 ( 5*6+ 6*7+ 5*7)

SA = 2(30+42+35)

SA = 2(107)

SA =214

Prism B

SA = 2 (lw+wh+lh) where l is length w is width and h is height

SA = 2 ( 10*12+ 12*14+ 10*14)

SA = 2(120+168+140)

SA = 2(428)

SA =856

Robert is not correct

856/214 =4

Prism B is 4 times greater