MATHEMATICS - FORM 2 SOLID GEOMETRY II GEOMETRIC PROPERTIES OF PRISMS, PYRAMIDS, CYLINDERS, CONES AND SPHERES (A) Stating the geometric properties of prisms, pyramids, cylinders, cones and spheres 1. Prisms (a) A prism is a solid with two congruent, parallel bases which are polygons. The other faces called lateral faces are in the shape of parallelograms.
Solid Geometry Form 2
Oct 31, 2014
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MATHEMATICS - FORM 2
SOLID GEOMETRY II
GEOMETRIC PROPERTIES OF PRISMS, PYRAMIDS, CYLINDERS, CONES AND SPHERES(A) Stating the geometric properties of prisms, pyramids, cylinders, cones and spheres
1. Prisms (a) A prism is a solid with two congruent, parallel bases which are polygons. The other faces called lateral faces are in the shape of parallelograms.
(b) A prism has a uniform cross section in the shape of a polygon. (A section if the cross sections have the same shape and area as the end faces of the solid.)
(c) A right prism is a prism in which the bases of the prism are perpendicular to the bases of the prism are perpendicular to the prism are perpendicular to the lateral faces.
(d) The type of prism is named after the shape of its base.
(i) (ii)
Triangular prism Rectangular prism
(iii) (iv)
Pentagonal prism Hexagonal prism
(e) Example : A triangular building block
2. Pyramid (a) A pyramid is a solid with a flat base in the shape of a polygon, and triangular faces that converge at a vertex. (b) A right pyramid has its vertex directly above the centre of its base.
(c) The type of pyramid is named after the shape of its base.
(i) (ii)
Triangular pyramid Square pyramid
(iii) (iv)
Rectangular pyramid Hexagonal pyramid (d) Example : Pyramid of Giza, Egypt. 3. Cylinder (a) A cylinder is a solid with two parallel congruent circular bases and a curved surface.
(b) Example: A milk tin, a plastic pipe
4. Cone (a) A cone is a solid with a circular base, a curved surface and a vertex.
(b) Example: An ice cream cone, a party hat
5. Sphere (a) A sphere is a solid whereby all its points on the surface are at the same distance from the centre.
(b) Example: A football, a marble
6. The geometric solids can be categorized into three groups. (a) Solids with flat surfaces only. Example: Cubes, cuboids, prisms and pyramids (b) Solids with curved surfaces only. Example: Spheres (c) Solids with both flat and curved surfaces Example: Cones and cylinders
NETS(A) Drawing NetsNet of a geometric solid is the shape in a plane that is obtained by opening up and flattening out the faces of the geometric solid.
Net of a geometric solid may have many different shapes.
Draw a net for each of the following geometric solids.(a) (b)
(c) (d)
(e) (f)
(a) (b)
(c) (d)
(e) (f)
(B) Stating the Types and Constructing Models of Solid Given Their Nets
The figure shows the net of a geometric solid.(a) State the type of solid formed from the net.(b) Copy the net according to the measurements given and then construct a model of the solid.
(a) cuboid(b)
(a) Name the solid which can be formed from the net shown.(b) Construct a model of the solid according to the measurements given.
(a) A right prism(b)
(a) State the type of solid that has the net shown in the figure.(b) Construct a model of the solid according to the actual measurement given.
(a) A right cylinder(b)
SURFACE AREA(A) Stating the surface area of prisms, pyramids, cylinders and cones
The surface area of a solid is the total area of all the faces of the solid. Therefore, the surface area of a solid can be calculated from its net.
(a) Prism (i) Triangular prism
Surface area of a triangular prism= 2 x Area of cross section + Total area of lateral faces= 2 (Area of triangle) + Total area of 3 rectangles (ii) Hexagonal prism
Surface area of a hexagonal prism= 2 x Area of cross section + Total area of lateral faces= 2 (Area of hexagon) + total area of 6 rectangles
(b) Pyramid (i) Triangular pyramid
Surface area of a triangular pyramid= Area of base + Total area of 3 triangular faces= Area of triangular base + Total area of 3 triangles
(ii) Rectangular pyramid
Surface area of a rectangular pyramid= Area of base + Total area of 4 triangular faces= Area of rectangular base + Total area of 4 triangles
(c) Cylinder
(d) Cone
(B) Finding the surface area of prisms, pyramids, cylinders and cones
Calculate the surface area for each of the following.
(a) (b) (c)
(d) (e) (f)
(C) Finding the surface area of spheres using the standard formula
The surface area of a sphere can be determined by using a formula.
The radius of the earth is approximately 6 400 km. Find the surface area of the earth.
(D) Finding the dimensions of a solid given its surface area
(E) Solving problems involving surface area
The diagram shows a solid consisting of a cuboid and a right cylinder with one end of the cylinder resting on top of the cuboid. The cylinder has a diameter of 28 cm and a height of 10 cm. Determine the total surface area of the solid.
The diagram shows a closed cylindrical tank. Draw the net for the cylindrical tank.
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