Extending To Three Dimensions Plato Post Test 100% Pass

Extending To Three Dimensions Plato Post Test 100% Pass Prism M and pyramid N have the same base area and the same height. Cylinder P and prism Q have the same height and the same base perimeter. Cone Z has the same base area as cylinder Y, but its height is three times the height of cylinder Y. The figures prism M cylinder P cone Z and pyramid N prism Q cylinder Y have the same volume. -Cone Z -Cylinder Y Among these figures, figure (A C E) and figure (B D) have the same volume. -C -D A cone is placed inside a cylinder. The cone has half the radius of the cylinder, but the height of each figure is the same. The cone is tilted at an angle so its peak touches the edge of the cylinder's base. What is the volume of the space remaining in the cylinder after the cone is placed inside it? 3/4 (pi r^2 h) The cone in the diagram has the same height and base area as the prism. What is the ratio of the volume of the cone to the volume of the prism? 1/3 The height of the pyramid in the diagram is three times the radius of the cone. The base area of the pyramid is the same as the base area of the cone. What is the expression for the volume of the pyramid in terms of the radius r of the cone? pi r^3. The base of the prism in the diagram is rectangular, but the edges that are not parallel to the base are tilted. What is the volume of the prism? 648cm3 A pyramid has a square base with side s. The height of the pyramid is that of its side. What is the expression for the volume of the pyramid? V= 2 / 9s ^3 Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption, the volume of the flask is 20.2235.0850.07100.11 cubic inches. If both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be 2468 times the original volume. -5.07 -8 The volume of clay used to build a cylindrical pillar with a height of 9 centimeters is 324π cubic centimeters. The area of the base of the pillar is ???π square centimeters. 36 An artist wants to make alabaster pyramids using a block of alabaster with a volume of 576 cubic inches. She plans to make each pyramid with a square base area of 3 square inches and a height of 4 inches. At most, how many pyramids can the artist make from the block of alabaster? 144 pyramids A satellite launch rocket has a cylindrical fuel tank. The fuel tank can hold V cubic meters of fuel. If the tank measures d meters across, what is the height of the tank in meters? Height = ( 4V ) / ( pi d² ) A candle manufacturer sells cylindrical candles in sets of three. Each candle in the set is a different size. The smallest candle has a radius of 0.5 inches and a height of 3 inches. The other two candles are scaled versions of the smallest, with scale factors of 2 and 3. How much wax is needed to create one set of candles? 86 cubic inches An action movie production team needs glass spheres to hold a green liquid that looks like an explosive. If all of the available 3,392.92 cubic inches of the liquid is to be poured into 30 glass spheres, what should the diameter of each sphere be? Assume that each sphere is filled to the top. 6 inches The radii of Earth and Pluto are 6,371 kilometers and 1,161 kilometers, respectively. Approximately how many spheres the size of Pluto does it take to have the same volume as Earth? 165 A hexagonal pyramid is cut by a plane as shown in the diagram. What is the shape of the resulting cross section? A hexagon This two-dimensional shape can be created by rotating a cylinder pyramidrhombustrapezoid about its base. Another two-dimensional shape that can give this shape is a hexagonpentagonrectangletriangle rotated about a line joining two opposite vertices. -Trapezoid -Pentagon A plane intersects a prism to form a cross section that is a polygon with five sides. The minimum number of sides that the polygon at the base of the prism must have is ??? 4 The base of a cube is parallel to the horizon. If the cube is cut by a plane to form a cross section, under what circumstance would it be possible for the cross section be a non-rectangular parallelogram? when the plane passes through a pair of vertices that do not share a common face A pentagonal prism is cut by a plane perpendicular to the base. What is the shape of the cross section that is formed? A rectangle