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Presented to: Mg* Diego Leandro León By: German Avila Mendoza - THE PRISM Andrea Maria Rincon - THE PIRAMID Sandra Patricia Mira - THE CYLINDERMelisa Betancur Lezcano - THE CONE Maria Judith Ruiz - THE SPHERE Geometric Solid November 30, 2020 ¿What are the main elements of the prisms? Bases: They all have two bases, both being equal and parallel. Side faces: They are the parallelograms between the 2 bases. Height: It is the distance between the two bases. ¿ what are prisms ? A prism is a polyhedron that has two equal and parallel faces called bases and their lateral faces are parallelograms. THE PRISM Imagen Pinterest.es Main elements of prisms Height Base Base Side face Pentagonal ¿What types of prisms are there according to their base? Irregular: Are those whose bases are irregular polygons. Regular: They are those whose bases are regular polygons. The prisms take the name of the base polygon: Quadrangular Triangular Hexagonal To calculate the area of the prism, add the area of each of the faces you have. For right prisms, the area is calculated as follows: Area = 2 × Ab + Pb × h where Ab is the area of the base Pb is the perimeter of the base h is the height of the prism Prism Area You need to build the school's sports badge from the El Silencio village in the Municipality of Cisneros,and a philanthropist donates financial resources. The plate will be built in the shape of a rectangular prism, its measurements being 18 m long, 12 m wide and 6 m thick. What is the total area of the rectangular prism? Rectangular prism 6 m 18 m 12 m 1 First of all, we calculate the perimeter of the base of the plate, which because it is a rectangle, we must calculate its surface, as the plate is a rectangular prism, we find its total area, for this we need to know the perimeter of the base, the lateral area and the base area PBase = 2*12 m + 2*18 m = 60 m 2 The total area is given by the sum of the lateral area and twice the area of the base, that is, AT = AL + 2 AB. We calculate the lateral area AL = 6 m * 60 m = 360 m2 3. We calculate the area of the baseAB = 12 m * 18 m = 216 m2 4. We have the values of the lateral and base area, with them we calculate the total areaAT = 360 m2 + 2 * 216 m2 = 792 m2 The Pyramid It is a polyhedron with a three-dimensional shape that is made up of a base and triangular lateral faces where the edges meet at a point known as the common vertex. Elements of the pyramid Classification of pyramids according to the polygon of their base Is the portion of the pyramid between the base and a plane parallel to it that intersects all the lateral artists. The height of the trunk is a segment perpendicular to the planes of the two bases. The resulting segment of apothem of the pyramid is the apothem of the trunk. Pyramid trunk What is the volume of a pyramid with a quadrangular base, if the sides of the base measure 10 cm and the height is 18 cm. Volume of the pyramid Select the correct option V=1/3 B . h a. 600 m3 b. 610 m3 c. 580 m3 d. 660 m3 Find the total area of a quadrangular pyramid with a side of base 10 m and height 5 m. Pyramid area A lateral = sum of lateral faces. A total = A lateral + A Base Select the correct option a. 241,4 m2 b. 441,4 cm2 c. 641,4 cm2 d. 541,4 cm2 THE CYLINDER Is a round geometric solid,formed by a rectangule and two parallel base circles. FLAT DEVELOPMENTTwo circles of equal size and a rectangle whase width is equal to the length of the circle. CYLINDER ELEMENTS AREA AND VOLUMEh=heightr= radiusVolume: area of base times height What is the area of the cylinder knowing that h = 9 cm and r = 3 cm? 2.260 cm2 22.60 cm2 226.08 cm2 2.260.08 cm2 What is the volume of a cylinder knowing that h = 9 cm and r = 3 cm? 1.160 cm3 116 cm3 1.161 cm3 6.111 cm3 It is the body of revolution obtained spinning a right triangle around one of his legs. HEIGHT: It is the distance from the vertex to the base. THE CONE AXIS: It is the fixed leg around which the triangle rotates. CONE ELEMENTS VERTEX: is the point where the generatrices converge GENERATOR: It is the hypotenuse of the right triangle. BASE: It is the circle that forms the other leg. To calculate the area or volume you only need one cone two of the following 3 data: height, radius, generatrix, since by the theorem Pythagoras can be find the third. Regarding volumes and how it happened with the prism and the inscribed pyramid, the volume of the cone is one third of the volume of the cylinder of equal base and height. CONE AREA AND VOLUME 50,24 cm3 94,2cm3 Determine the volume of a 4-cm cone of a ice cream radius and 3cm tall 62,8 cm3 39,6 cm3 Determine the total area of an ice cream cone 4cm radius and 3cm high 113,04 cm3 175,84 cm3 94,2 cm3 THE ELEMENTS OF THE CONE ARE: BASE, HEIGHT, RADIO, GENERATOR Y VERTICE Imagen. Recursostic.educación.es FALSE TRUE THE CONE IS A BODY FORMED FORMED BY A LATERAL AND CLOSED CURVED SURFACE AND TWO PARALLEL PLANES THAT FORM ITS BASES; ESPECIALLY THE CIRCULAR CYLINDER. TRUE FALSE Imagen. Gifimagen.net Geometrical body of revolution formed by rotating a semicircle around its diameter. THE SPHERE EXAMPLES Maximum circumference: Circumference drawn on the sphere and whose center is the same center of the sphere. SPHERE ELEMENTS Rotating axis: Line where the diameter of the semicircle is located. Center: Interior point equidistant from any point on the sphere. Diameter: Line segment that passes through the center (rotating axis) of the sphere and joins two opposite points located on its surface. Radius: Distance from the center to a point on the sphere. Area of the sphere: Surface that surrounds this solid of revolution. Volume of the sphere: It is the space that the sphere occupies, or thefilling capacity it has. AREA AND VOLUME OF THE SPHERE Ana wants to give her classmates a ball of chocolate for “love and friendship”. She has a mold to make the balls that has 2 cm of radius. She needs to know with how much melted chocolate she must fill the mold to make a sphere or chocolate ball. After making the balls, she wants to wrap them in foil without wasting it. How much foil does she need in order to wrap a ball? MATH PROBLEM To find out how much chocolate is needed to fully fill the mold, we calculate the volume as follows: And to know how much paper we need to wrap a ball without wasting it we calculate the area: |