Questions from General Calculus

Q: Each integral represents the volume of a solid. Describe the solid

Each integral represents the volume of a solid. Describe the solid.

Q: A CAT scan produces equally spaced cross-sectional views of a

A CAT scan produces equally spaced cross-sectional views of a human organ that provide information about the organ otherwise obtained only by surgery. Suppose that a CAT scan of a human liver shows cr...

Q: Sketch the region enclosed by the given curves. Decide whether to

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the reg...

Q: A log 10 m long is cut at 1-meter intervals

A log 10 m long is cut at 1-meter intervals and its cross- sectional areas A (at a distance x from the end of the log) are listed in the table. Use the Midpoint Rule with n = 5 to estimate the volume...

Q: (a) If the region shown in the figure is rotated

(a) If the region shown in the figure is rotated about the x-axis to form a solid, use the Midpoint Rule with n = 4 to estimate the volume of the solid. (b) Estimate the volume if the region is rot...

Q: (a) A model for the shape of a bird’s egg

(a) A model for the shape of a bird’s egg is obtained by rotating about the x-axis the region under the graph of Use a CAS to find the volume of such an egg. (b) For a red-throated l...

Q: Find the volume of the described solid S. A right

Find the volume of the described solid S. A right circular cone with height h and base radius r

Q: Find the volume of the described solid S. A frustum

Find the volume of the described solid S. A frustum of a right circular cone with height h, lower base radius R, and top radius r

Q: Find the volume of the described solid S. A cap

Find the volume of the described solid S. A cap of a sphere with radius r and height h

Q: Find the volume of the described solid S. A frustum

Find the volume of the described solid S. A frustum of a pyramid with square base of side b, square top of side a, and height h What happens if a = b? What happens if a = 0?