A rectangular solid P has height 2c and a base of width a and length b. Two otherrectangular solids, Q and R, each have height c and bases of width a and length b. Whichof the following represents the amount by which the sum of the surface areas of Q andR exceeds the surface areas of P? A. 2abB. 4abC. 2ab + 2bcD. 2ab + 4acE. 2ab + 4ac + 4bc

A. 2ab

Step-by-step explanation:

For solid P with height 2c and a base of width a and length b,

Total surface area = 2 (2ca + 2cb + ab)

For the two other rectangular solids, Q and R, each have height c and bases of width a and length b

Total surface area of Q = 2 (ca + cb + ab)

Total surface area of R = 2 (ca + cb + ab)

Total surface area of the two solids = 2 (ca + cb + ab) + 2 (ca + cb + ab)

= 4 (ca + cb + ab)

Difference between sum of the surface areas of Q and R and the surface area of P

= 4 (ca + cb + ab) - 2 (2ca + 2cb + ab)

= 4ca + 4cb + 4ab - 4ca - 4cb - 2ab

= 4ca - 4ca + 4cb - 4cb + 4ab - 2ab

= 2ab

The sum of the surface areas of Q and R exceeds the surface areas of P by 2ab. Option A