The base of a solid in the region bounded by the two parabolas y2 = 8x and x2 = 8y. cross sections of the solid perpendicular to the x-axis are semicircles. what is the volume, in cubic units, of the solid?

288 times pi over 35

576 times pi over 35

144 times pi over 35

8π

The two curves intersect at two points, (0, 0) and (8, 8):

The area of a semicircle with diameter is . The diameter of each cross-section is determined by the vertical distance between the two curves for any given value of between 0 and 8. Over this interval, and , so the volume of this solid is given by the integral

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.