Key Concept

  • Solid figures:3D shapes which occupy some space are called Solid Figures. Example - Cube, Cuboid, Sphere etc.
  • Volume:Space occupied by any solid shape is the capacity or volume of that figure. The unit of volume is a cubic unit.
  • Surface Area:The area of all the faces of the solid shape is the total surface area of that figure. The unit of surface area is a square unit.
  • 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.

Surface Area and Volume of a Cube:Cube is a solid shape having 6 equal square faces.

Surface Area and volume of a Cuboid: Cuboid is a solid shape having 6 rectangular faces at a right angle.

Surface Area and Volume of a Right Circular Cylinder
If we fold a rectangular sheet with one side as its axis then it forms a cylinder. It is the curved surface of the cylinder. And if this curved surface is covered by two parallel circular bases then it forms a right circular cylinder.

Surface Area and Volume of a Hollow Right Circular Cylinder
If a right circular cylinder is hollow from inside then it has different curved surface and volume.

Surface Area and Volume of a Right Circular Cone
If we revolve a right-angled triangle about one of its sides by taking other as its axis then the solid shape formed is known as a Right Circular Cone.

Surface Area and Volume of a Sphere
A sphere is a solid shape which is completely round like a ball. It has the same curved and total surface area.

Surface Area and Volume of a Hemisphere
If we cut the sphere in two parts then is said to be a hemisphere.

Question: A hemi- spherical dome of a building needs to be painted. If the circumference of the base of the dome is 17.6 m, find the cost of painting it, given the cost of painting is Rs. 5 per 100cm2.

Solution:


circumference of the base of dome (r)=17.6m

Radius=c2π=17.6×72×22=2.8m

Surface area=2πr2=2×227×(2.8)2m2=447×2.8×2.8m2=49.28m2

Rate of painting the surface=Rs.5 per 100 cm2

Total cost=49.28×5×10000100=Rs.24640

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