Mathematics

Problem

Let

R

be the region in the first quadrant bounded by

y=4-x^{2}

, the

x

–axis, and the lines

x=0

and

x=2

. • Solid

S

is built on

R

with cross sections perpendicular to the

x

–axis that are squares. • Solid

T

is built on the same base

R

with cross sections perpendicular to the

x

–axis that are rectangles whose height is twice the length of the side that lies in

R

. Identify which solid,

S

T

, has the greater volume and state a brief reason.