Surface Areas and Volumes

%%Solids%%

Any object occupying fixed space and volume is called a solid. For example: cube, cuboid, sphere, cylinder, cone etc.

%%Surface area of a Solid%%

The area occupied by a solid object is known as surface area. The unit of surface area is taken as square unit. Example - square meter (m^2)

%%Volume of a solid%%

The measure of the occupied space is called volume of a solid. The unit of volume is cubic unit. Example - cubic meter (m^3)

%%Lateral or Curved Surface Area%%

The surface area of the solid shape after leaving the top and bottom face of the figure is called the lateral surface of the shape. The unit of lateral surface area is a square unit.

%%Right Circular Cylinder%%

A right circular cylinder is a closed solid that has @@two parallel circular bases connected by a curved surface@@ in which the two bases are exactly over each other and the axis is at @@right angles to the base.@@

  • Curved surface area of a right circular cylinder = 2πrh
  • Total surface area of a right circular cylinder = 2πr(r + h)
  • Volume of a right circular cylinder = πr^2h

%%Right Circular Cone%%

A right circular cone is a circular cone whose axis is perpendicular to its base.

  • Curved surface area of a right circular cone = πrl
  • Total surface area of a right circular cone = πr(l + r)
  • Volume of a right circular cone = 1/3 πr^2h

The relationship between the slant height (l) and height (h) of a right circular cone is l^2 = h^2 + r^2, where r is the radius of the base of the cone

%%Sphere%%

The three-dimensional solid obtained from collection of all the points in space lying at the @@constant distance@@ called as radius, from the fixed point called centre, is known as sphere.

  • Surface area of a sphere = 4πr^2
  • Volume of a sphere = 4/3 πr^3

%%Hemisphere%%

When a plane slices a solid it into two equal parts, @@passing through the centre@@, then each part is called a hemisphere.

  • Curved surface area of a hemisphere = 2πr^2
  • Total surface area of a hemisphere = 3πr^2
  • Volume of a hemisphere = 2/3 πr^3

%%Note%%

  • Area × Rate = Cost
  • Density = Mass/Volume
  • 1 m^3 = 1000 litres
  • 1 L = 1000 cm2
  • Speed = Distance/Time
  • 1 km = 1000 m = 105 cm
  • 1 km^2 = 106 m^2
  • 1 m = 100 cm
  • 1 m^2 = 10000 cm^2
  • 1 km/hr = 5/18 m/sec
  • 1 km/hr = 50/3 m/min
  • Shape of the river = cuboid