Geometry Enriched Study Guide - Chapter 10 Spatial Reasoning Right Prism Right Cylinder Lateral Area (L) Ph 2π rh Surface Area L + 2B L + 2π r 2 Volume (right, oblique & non-regular) Bh π r 2h Regular Pyramid 1 2 Sphere π r ----- L + πr2 4π r 2 P L+B 1 3 Right Cone Bh 1 3 π r 2h 4 3 πr3 Vocabulary face - the flat surface of a 3D figure edge - the segment that is the intersection of two faces lateral face - a face which is not a base net - a diagram of the surfaces of a 3D figure that can be folded to form the figure cross-section - the intersection of a 3D figure and a plane surface area - the total area of all faces and curved surfaces of a 3D figure lateral area - the sum of the lateral face areas prism - formed by two parallel congruent polygonal bases connected by parallelogram faces base of prism - a face of a prism which is congruent and parallel to another face of the same prism right prism - a prism in which all lateral faces are rectangles oblique prism - a prism in which at least one face is not rectangular cylinder - formed by two parallel congruent circular bases connected by a curved surface base of cylinder - one circular face of a cylinder axis of a cylinder - the segment which connects the centers of the cylinder bases right cylinder - a cylinder in which the axis is perpendicular to the base oblique cylinder - a cylinder in which the axis is not perpendicular to the base pyramid - formed by a polygonal base with triangular faces that connect the base to a vertex regular pyramid - a pyramid in which the base is a regular polygon and the lateral faces are congruent isosceles triangles non-regular pyramid - a pyramid in which the lateral triangular faces are not congruent slant height l of a pyramid - distance from the vertex to the midpoint of a base edge altitude - distance from the top vertex to the plane containing the base cone - formed by a circular base with a curved surface that connects the base to a vertex slant height l of a cone - distance from the vertex to the base edge of a cone axis of a cone - the segment which connects the cone’s vertex to the center of the base right cone - a cone in which the axis is perpendicular to the base oblique cone - a cone in which the axis is not perpendicular to the base sphere - a locus of points in space equidistant from a fixed point hemisphere - half of a sphere great circle - divides a sphere into two hemispheres Net of triangular prism Geometry Enriched! Chapters 10 Review Problems! Name ________________________________ Date ____________________ Period ______ 1) Find the volume and surface area of the composite figure below. 2) A square pyramid has a slant height of 17 cm and a lateral area of 544 sq cm. What is the volume? 3) Find the volume of a sphere with surface area 196π km square. Keep in terms of π. 4) In the cube figure, find the diagonal length d when e=3. 5) The length of a right rectangular prism is twice the width, and the height is three times the width. If the volume is 162 cm cubed, find the total surface area of the solid. 6) Find the volume of a regular hexagonal pyramid with height 8 cm and base edges 6 cm. 7) A solid metal cylinder with radius 6 cm and height 18 cm is melted down and recast as a solid cone with radius 9 cm. Find the height of the cone. 8) A hemispheric bowl with radius 25 contains water whose depth is 10. What is the area of the water’s surface?
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