Important concepts, chapter 4 , SSLC maths

Chapter 4 Solids

Important concepts

1. Square Pyramid
• A square pyramid has a square base and four lateral faces . The lateral
faces can be isoceles triangles or equilateral triangles. The sum of the areas
of the these triangles is called lateral face area of the pyramid.lateral face
area is the half of the product of base perimeter and slant height.The sum
of the lateral face area and base area is called total surface area. Volume of
the pyramid is one third of the base area and height
• The slant height ,height and half of base edge form a right angle triangle
Height , half of base diagonal and lateral edge makes a right triangle. The
slant height , half of base edge and lateral edge form a right triangle
• Cone
• Base is a circle . Lateral surface is curved . Sum of these two makes the total
surface area. Curved surface area is half the product of base pemimeter and
slant height. Volume is one third of the product of base area and height
• Slant height , radius and height form a right triangle
• A cone can be made by folding a sectoral sheet of paper . While doing so,
the radius of the sector becomes the slant height of the cone. The arc length
of the sector becomes the base parimeter of the cone. Area of the sector
becomes curved surface area of the cone
• What fraction of the central angle of the sector is to 360◦
is equal to fraction
of arc length of the sector to the perimeter of the circle from which sector
is taken off
2. Sphere and Hemisphere
• A sphere has only one face. Its basic measure is radius . Curved surface
area is the product of 4π and the square of radius . Volume of the sphere
is 4/3π×( r×r×r)
• A solid hemisphre has a curved surface and a circular plane surface. Curved
surface area of the hemisphere is 2π(r×r)
, total surface area 3π(r×r)
, volume is 2/3×π×(r×r×r)