P Preliminary Concepts 1 Line And Angle Relationships 2 Parallel Lines 3 Triangles 4 Quadrilaterals 5 Similar Triangles 6 Circles 7 Locus And Concurrence 8 Areas Of Polygons And Circles 9 Surfaces And Solids 10 Analytic Geometry 11 Introduction To Trigonometry A Appendix Chapter9: Surfaces And Solids
9.1 Prisms, Area And Volume 9.2 Pyramids, Area, And Volume 9.3 Cylinders And Cones 9.4 Polyhedrons And Spheres 9.CR Review Exercises 9.CT Test Section9.3: Cylinders And Cones
Problem 1E: Does a right circular cylinder such as an aluminum can have a symmetry with respect to at least one... Problem 2E: Does a right circular cone such as a wizards cap have a symmetry with respect to at least one plane?... Problem 3E Problem 4E Problem 5E: For the right circular cylinder, suppose that r=5 in. and h=6 in. Find the exact and approximate a... Problem 6E: Suppose that r=12 cm and h=15 cm in the right circular cylinder. Find the exact and approximate a... Problem 7E: The tin can shown at the right has the indicated dimensions. Estimate the number of square inches of... Problem 8E Problem 9E: If the exact volume of a right circular cylinder is 200cm3 and its altitude measures 8 cm, what is... Problem 10E: Suppose that the volume of an aluminum can is to be 9in3. Find the dimensions of the can if the... Problem 11E: For an aluminum can, the lateral surface area is 12in2. If the length of the altitude is 1 in.... Problem 12E: Find the height of a storage tank in the shape of a right circular cylinder that as a circumference... Problem 13E: Find the volume of the oblique circular cylinder. The axis meets the plane of the base to form a 45... Problem 14E: A cylindrical orange juice container has metal bases of radius length 1 in. and a cardboard lateral... Problem 15E Problem 16E: In Exercises 15 to 20, use that fact that r2+h2=l2 in a right circular cone Theorem 9.3.6. Find the... Problem 17E Problem 18E: In Exercises 15 to 20, use that fact that r2+h2=l2 in a right circular cone Theorem 9.3.6. Find the... Problem 19E Problem 20E Problem 21E: The oblique circular cone has an altitude and a diameter of base that are each of length 6 cm. The... Problem 22E: For the accompanying right circular cone, h=6 m and r=4 m. Find the exact and approximate a lateral... Problem 23E Problem 24E: Rukia discovers that the teepee with a circular floor has a radius length of 6 ft and a height of 15... Problem 25E Problem 26E Problem 27E Problem 28E: A triangle has sides that measure 15 cm, 20 cm, and 25 cm. Find the exact volume of the solid of... Problem 29E Problem 30E Problem 31E: If a right circular cone has a circular base with a diameter of length 10 cm and a volume of 100cm3,... Problem 32E: A right circular cone has a slant height of 12 ft and a lateral area of 96ft2. Find its volume. Problem 33E: A solid is formed by cutting a conical section away from a right circular cylinder. If the radius... Problem 34E Problem 35E: In Exercises 34 and 35, give a paragraph proof for each claim. The volume V of a washer that has an... Problem 36E: For a right circular cone, the slant height has a measure equal to twice that of the radius length... Problem 37E: For a right circular cone, the ratio of the slant height to the length of the radius is 5:3. If the... Problem 38E: If the length of the radius and the height of a right circular cylinder are both doubled to form a... Problem 39E Problem 40E: For a right circular cone, the dimensions are r=6 cm and h=8 cm. If the length of the radius is... Problem 41E: A cylindrical storage tank has a depth of 5 ft and a radius measuring 2 ft. If each cubic foot can... Problem 42E: If the tank in Exercises 41 needs to be painted and 1 pint of paint covers 50ft2, how many pints are... Problem 43E: A frustum of a cone is the portion of the cone bounded between the circular base and a plane... Problem 44E: In Exercises 44 and 45, use the formula from Exercise 43. Similar triangles were used to find h and... Problem 45E: In Exercises 44 and 45, use the formula from Exercise 43. Similar triangles were used to find h and... Problem 46E Problem 47E: Richard has a fuel tank in the shape of a right circular cylinder. The tank has a height of 6 ft and... Problem 48E: When radii OA and OB are placed so that they coincide, a 240 sector of a circle is sealed to form a... Problem 49E: A lawn roller in the shape of a right circular cylinder has a radius of length 18 in. and a length... Problem 25E
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Set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the x -axis.
y = 25 − x 2
Transcribed Image Text: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the x-axis.
y = 25 – x2
25
20-
15
y
10-
5-
4
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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