Nothing Special   »   [go: up one dir, main page]
Scribd Logo
Upload

Welcome to Scribd!

  • 3 views

    Mensuration

    Uploaded by

    techwithdeepak01

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd

    Mensuration

    Uploaded by

    techwithdeepak01
    3 views18 pages

    Copyright

    © © All Rights Reserved

    Available Formats

    PPTX, PDF, TXT or read online from Scribd

    Did you find this document useful?

    Is this content inappropriate?

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    3 views18 pages

    Mensuration

    Uploaded by

    techwithdeepak01

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    of 18

    Mensuration

    Done by T.V.N.K. Sreevasthav


    Introduction
    • Mensuration is the branch of geometry
    that deals with the measurement of
    area, length, or volume in 2D and 3D
    shapes. The 2D shapes can be drawn in
    a plane like square, rectangle, triangle,
    circle, etc. and 3D shapes cannot be
    represented in a plane like bricks, ice-
    cream cones, football, etc. Mensuration
    includes computation using
    mathematical formulas and algebraic
    equations.
    2D-Shapes
    • RECTANGLE:- Area- lxb sq.units
    Perimeter – 2(l+b) units
    • TRIANGLE:- Area - x b x h sq.units

    Perimeter – Sum Of All Sides. units


    • SQUARE:- Area – a x a sq.units
    Perimeter – 4 x a units
    • CIRCLE:- Area - sq.units
    Some 3D shapes

    Cube Cuboid Sphere Cylinder Cone


    CUBE
    CUBE
    A cube is a 3-D solid Some Formulae
    shape, which has 6 faces.
    A cube is one of the • Surface Area of Cube = 6a2 square units
    simplest shapes in three- • Volume of cube = a3 cubic units
    dimensional space. All • Lateral Surface Area = 4a2 square units
    • Length of Diagonal of Face of the Cube = √2 a units
    the six faces of a cube • Length of Diagonal of Cube = √3 a units
    are squares
    CUBOID
    CUBOID
    • A cuboid is a three dimensional solid that has 6 Some Formulae
    faces (rectangular), 8 vertices and 12 edges. A
    cuboid has three dimensions such as length,
    width and height. A perfect cuboid is said to be a
    cuboid that has integer edges.
    • Lateral Surface Area (LSA) = 2h(l + b) sq. units
    • Consider Euler’s formula, then the relation • Total surface area TSA = 2( lb + bh + hl ) sq. units
    between Faces (F), Vertices (V) and Edges (E) of • Volume = lbh cubic units
    a cuboid satisfies the equation: • Perimeter = 4(l + b + h) units
    F+V=E+2 • Diagonal = √(l^2 + b^2 + h^2) units
    SPHER
    E
    SPHERE
    A sphere is three dimensional,
    geometrical shape, that has all its Some Formula
    surface points equidistant from a
    common point. The distance • Surface Area = Square units
    between the surface and the common • Volume = cubic units
    point is the radius and the common
    point is called center of sphere.
    HEMI -
    SPHERE
    Hemi-Sphere

    The word hemisphere can be separated into Some Formulae


    hemi, which denotes half, and sphere,
    which refers to the geometrical 3D shape in • Curved surface area of a hemisphere = 2
    mathematics. Consequently, a hemisphere • Area of base =
    is a 3D geometric object that is made up of • Total Surface Area = 3
    half of a sphere, with one side being flat
    • Volume of hemisphere =
    and the other being a bowl-like shape.
    CYLINDER
    CYLINDER
    A cylinder is a three-dimensional solid that Some Formulae
    holds two parallel bases joined by a curved
    surface, at a fixed distance. These bases are • Curved Surface Area = 2πrh square units
    • Total surface area = 2πr(r+h) square units
    normally circular in shape and the center of • Volume of the Cylinder = πr2h cubic units
    the two bases are joined by a line segment,
    which is called the axis. The perpendicular
    distance between the bases is the height, “h”
    and the distance from the axis to the outer
    surface is the radius “r” of the cylinder.
    CONE
    Cone
    A pyramid which has a circular Some Formulae

    cross-section, unlike pyramid • Slant Height = √(r2+h2) units


    which has a triangular cross- • Volume = ⅓ πr2h cubic units
    • Total Surface Area = πr(l + r) sq. units
    section. These cones are also
    stated as a circular cone.
    Some Questions on
    Mensuration
    1. 1. A circle has a radius of 21 cm. Find its circumference and
    area. (Use π = 22/7).
    2. If one side of a square is 4 cm, then what will be its area
    and perimeter?
    3. If a cube has its side-length equal to 5cm, then its area is? For Answers

    4. Find the height of a cylinder whose radius is 7 cm and the


    total surface area is 968 cm2.
    5. Find the height of a cuboid whose volume is 275 cm3 and
    base area is 25 cm2.
    6. A rectangular piece of paper 11 cm × 4 cm is folded
    without overlapping to make a cylinder of height 4 cm.
    Find the volume of the cylinder.
    OR
    Go to the link below for answers

    https://cutt.ly/mensurationanswers

    You might also like