Find the volumes of the solids generated by revolving the region between y = 2√x and y=- about a) the x-axis and b) the y-axis. 6

iv) The region bounded by the semi-circle x = centroid (x,y). a) Explain why y = 0. b) Find the centroid (x, 0). √√1 - y² and the y axis has

shape 4. A sphere x² + y² + z² ≤ 4a² has a hole drilled through it in the shape x² + y² ≤ 2ax. How much of the spherical volume is left afterwards? be usen

Can you please help me answer this two-part question?

Find the centroid of the region cut from the first quadrant by the circle x² + y² = 81. The coordinates of the centroid are (x,y) = (Type an ordered pair. Type an exact answer, using □ as needed.)

Ex10: A solid has its base, R, formed by x = y² - 3 and x = y + 1 in the xy-plane. Find the volume of the solid that has R as its base if every cross section by a plane perpendicular to the y-axis has the given an a) Equilateral triangle b) Rectangle with height 3

A vertical dam has the form of an isosceles trapezoid with horizontal sides parallel. The dam is 20 m high, 20 m in its lower part and 40 m in its upper part. Finally, the dam retains 15 m of water, as indicated in the figure below. 20 - 20 15 a) Let y denote the height in meters measured from the base of the dam. The hydrostatic force exerted by the water on the portion of the dam comprised between y m and y + Ay m is approximately p (y) Ay N. What is p (y)? Note that the density of water is p = 1000 Kg/m³ and the acceleration due to gravity on the earth's surface is g = 9.8 m/s2 Express your answer as a formula Answer: b) in Newtons, what is the total hydrostatic force exerted on the dam? FORMATTING: If you round your answer, ensure that the round-off error is less than 1% of the value. Answer Number