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Important Points in PrismThe side portion of a solid are called lateral surfaces. A solid is a three dimensional object.
2. A prism is polyhedron with two identical ends such that the lines joining the corresponding vertices of the two ends are all parallel. 3. Right Prism: A prism whose bases are perpendicular to the lateral edges and all lateral faces are rectangles is called right prism. 4. A prism is named according to the shape of its base. If the base of a prism is a triangle, then the prism is called triangular prism. 5. Number of lateral surfaces of a right prism = Number sides of the base of the prism. 6. Total number of surfaces of a prism = Number of lateral surfaces + 2. 7. Number of edges of a prism = 3 * Number of sides. 8. Sum of the lengths of edges = Number of sides * height + twice the perimeter of the base. That is S = n*h + 2s. 9. Lateral surface of a prism = Perimeter of the base * height. That is, A = p * h.
10. If 'a' is the side of cube.
11. If l is the length, b is the breadth and h is height of a cuboid.
12. In triangular prism. 14. The area of a equilateral triangle = (Ö3/4)a^{2}. Where a is the side of the triangle. 15. The area of a right angled triangle = 1/2 * ab, Where a, b are the sides containing right angle. 16. The area of a right angled isosceles triangle = 1/2*a^{2}.
17. The area of rhombus = 1/2 * d_{1} * d_{2}. Where d_{1}, d 18. Volume of cuboid = l * b * h cubic units. 19. Sum of the edges of a cuboid = 4(l + b + h) units. 20. Diagonal of a cuboid = Ö(l^{2} + b^{2} + h^{2}). 21. Volume of the cube = a^{3} cubic units.
Important Points in Cylinder2. The cylinder belongs to the family of prisms.
3. The curved surface area is equal to = Perimeter of the base * height
4. Area of the base of a cylinder = Area of circle.
5. Total surface area of a cylinder = Curved surface area + 2 * base area.
6. Volume of a cylinder = base area * height 7. A cycle tube is an example of a cylindrical shell which is neither a solid cylinder nor a hollow cylinder. 8. The ratio of curve surface area's of two cylinder of equal heights is equal to the ratio of their radii. 9. The ratio of the volumes of two cylinders of equal heights is equal to the ratio of squares of their radii. 10. The ratio of two curved surface area's of two cylinders of equal radii is equal to the ratio of their heights. 11. The ratio of the volumes of two cylinders of equal radii but of different heights is equal to the ratio of their heights. 12. If the volumes of two cylinders are equal, then the ratio of the squares of radii is inversely proportional to the heights of the cylinders. 13.The cross section by a vertical plane of a cylinder is a rectangle.
14. A right circular cylinder:
15. Axis of the cylinder:
16. Lateral surface:
17. Hollow cylinder:
18. Solid cylinder:
19. Cylindrical shell:
Important points in Cone2. Solid cone: It is the figure in space bounded by the curved surface of the cone and its plane circular end.
3. Curved surface area of a cone = pi * r * l, 4. Slant height, l^{2} = h^{2} + r2. 5. Lateral surface area of a cone is equal to pi * r * l.
6. Total surface area of a cone = Lateral surface area + Area of base, 7.Volume of a cone = 1/3 * pi * r^{2} * h. 8. A circus tent will be generally of the form of hollow cylinder surmounted by a cone. 9. Base of a cone: A cone has a plane surface circular in shape as base. 10. Vertex of cone: It is one end of the cone very far from the base.
Important Points in Sphere2. Any point on the surface of the sphere is equidistant from a fixed point in the interior of the sphere. This fixed point is called the centre of the sphere. 3. The line segment joining the centre of the sphere to any point on its surface is called the radius of the sphere.
4. As the sphere has only one surface namely curved surface its curved surface area and total surface area are not different. 5. Volume of sphere = 4/3 * pi * r^{3} 6. The volume of a sphere of radius r is equal to the volume of the cylinder whose base radius is also r and height (4/3)r.
7. A plane through the centre of the sphere divides the sphere into two equal parts and each is called a hemisphere. 8. A spherical shell can be regarded as the difference between two concentric spheres. 9. A spherical shell has a finite thickness which is the difference of the radii of the two solid spheres which determine it. Directions: Choose the correct answer. 