A Certain Solid S Has a Horizontal Plane Region R

Multiple Choice

A certain solid S has a horizontal plane region R as its base and has height h cm measured perpendicular to R. For 0 < z < h, the volume of that part of S lying beneath the plane at height z cm above R is V(z) = 2z + z³ cm³. Find (a) the area of the cross-section of S in the plane at height z cm and (b) the area of R.

A) (a) 2 + 3z² cm², (b) 2 cm²
B) (a) 1 + 3z² cm², (b) 1 cm²
C) (a) 3 + z² cm², (b) 3 cm²
D) (a) 2 + 4z² cm², (b) 3 cm²
E) (a) 1 + 2z² cm², (b) 1 cm²