MATHS PROJECT FA - II : MATHS PROJECT FA - II TOPIC SOLID SHAPES AND ITS VOLUME
PowerPoint Presentation : Group name - Aryabhatta Sagar, pritesh, vijay, kishan , govind CLASS – X B
contents : contents Parallelogram Triangle Rectangle Trapezoid Circle Rectangular Solid
PowerPoint Presentation : Prisms Cylinder Pyramid Cones Sphere Cuboids, Rectangular Prisms and Cubes right circular cylinder
PARALLELOGRAM : PARALLELOGRAM Parallelogram Area = Base X Height a = bh
Triangle : Triangle Triangle Area = 1/2 of the base X the height a = 1/2 bh Perimeter = a + b + c (add the length of the three sides)
Rectangle : Rectangle Rectangle: Area = Length X Width A = lw Perimeter = 2 X Lengths + 2 X Widths P = 2l + 2w
Trapezoid : Trapezoid Trapezoid Perimeter = area + b1 + b2 + c P = a + b1 + b2 + c
Circle : Circle Circle The distance around the circle is a circumference. The distance across the circle is the diameter (d). The radius (r) is the distance from the center to a point on the circle. (Pi = 3.14) More about circles. d = 2r c = pd = 2 pr A = pr 2 (p=3.14)
Rectangular Solid : Rectangular Solid Rectangular Solid Volume = Length X Width X Height V = lwh Surface = 2lw + 2lh + 2wh
Prisms : Prisms Prisms Volume = Base X Height v= bh Surface = 2b + Ph (b is the area of the base P is the perimeter of the base)
Cylinder : Cylinder Cylinder Volume = pr 2 x height V = pr 2 h Surface = 2p radius x height S = 2prh + 2pr 2
Pyramid : Pyramid Pyramid V = 1/3 bh b is the area of the base Surface Area: Add the area of the base to the sum of the areas of all of the triangular faces. The areas of the triangular faces will have different formulas for different shaped bases.
Cones : Cones Cones Volume = 1/3 pr 2 x height V= 1/3 pr 2 h Surface = pr 2 + prs S = pr 2 + prs =pr 2 + pr
Sphere : Sphere Sphere Volume = 4/3 pr 3 V = 4/3 pr 3 Surface = 4pr 2 S = 4pr 2
Spherical Shell : Spherical Shell Spherical Shell Solid enclosed between two concentric spheres is called a spherical shell. For a spherical shell if and are outer and inner radii respectively, then the volume of the shell is
PowerPoint Presentation : A cuboid is a box-shaped object. It has six flat sides and all angles are right angles . And all of its faces are rectangles. prism It is also a prism because it has the same cross-section along a length. In fact it is a rectangular . Cuboids, Rectangular Prisms and Cubes
PowerPoint Presentation : Cuboids
PowerPoint Presentation : Examples of Cuboids Cuboids are very common in our world, from boxes to buildings we see them everywhere. You can even fit them inside other cuboids!
Examples of cuboid : Examples of cuboid
Volume and Surface Area : Volume and Surface Area The volume of a cuboid is found using the formula: Volume = Height × Width × Length Which is usually shortened to: V = h × w × l Or more simply: V = hwl
Surface Area : Surface Area the surface area is found using the formula: A = 2wl + 2lh + 2hw Example: Find the volume and surface area of this cuboid. V = 4×5×10 = 200 A = 2×4×5 + 2×5×10 + 2×10×4 = 40+100+80 = 220
Square Prism : Square Prism When at least two of the lengths are equal it can also be called a square prism . (Note: this doesn't stop it from also being called a rectangular prism if you want!)
Square prism : Square prism
cube : cube If all three lengths are equal it can be called a cube (or hexahedron) and each face will be a square. A cube is still a prism. And a cube is one of the Platonic Solids .
PowerPoint Presentation : So: A cube is just a special case of a square prism, and A square prism is just a special case of a rectangular prism, and They are all cuboids!
right circular cylinder : right circular cylinder A right circular cylinder is a cylinder whose base is a circle and whose elements are perpendicular to its base
PowerPoint Presentation : Right circular cylinder
Properties of a Right Circular Cylinder : Properties of a Right Circular Cylinder The axis of a right circular cylinder is the line joining the centers of the bases. For any oblique or non-oblique sections which do not pass any one base, the center of which is at the axis. A right circular cylinder can be formed by revolving a rectangle about one side as axis of revolution. Every section of a right circular cylinder made by a cutting plane containing two elements and parallel to the axis is a rectangle.
Formulas for Right Circular Cylinder : Formulas for Right Circular Cylinder Area of the base, A b Lateral Area, A L Volume, V Total Area, A T Total area (open both ends), Total Area (open one end), Total Area (closed both ends),
PowerPoint Presentation : T hanks
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