The base of the solid s is the region bounded by the curves y = x 2 and y = 1, and cross-sections perpendicular to the x-axis are squares. find the volume of s!

Each cross section has a side length equal to the distance (parallel to the -axis) between the curves and , which is , and hence area of . The two curves intersect at and . Then the volume is equal to the integral

The integrand is even, since

so we can make use of symmetry to simplify this to

Computing the integral is trivial:

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.