Surface area and volumes for class 10th

PPt on surface areas of cube,cuboid, etc. suitable for class 9 or10

1. Surface areas and volumes

2. Group Members Shubham Vashishth Kulpreet Singh Aman Shrestha Prateek Diwakar Ritvik Gupta Rishabh J ain

3. Surface Area Surface area  is the total area of the faces and curved surface of the a solid figure. Mathematical description of the surface area is considerably more involved than the definition of  arc length  the surface area is the sum of the areas of its faces. Smooth surfaces, such as a  sphere , are assigned surface area using their representation as parametric surfaces . This definition of the surface area is based on methods of infinitesimal  calculus  and involves  partial derivatives  and  double integration .

4. Volume Volume is the measure of the amount of space inside of a solid figure, like a cube, ball,  cylinder  or  pyramid . It's units are always "cubic", that is, the number of little element cubes that fit inside the figure.  The formula for the volume of a rectangular prism is: Area = l x w x h where: l = length w = width h = height

5. Rectangular Pyramid Has rectangular base & 4 slanted faces. If the base is a square, & if the apex lies directly above a point at the center of the base, then it is a symmetrical square pyramid . S.A. = t 2 + 2t √(s 2 – t 2 /4) V = Ah/3 s = slant height t = edge of the base

6. The Cube It is a regular hexahedron Has 12 edges & 6 faces S.A. = 6s 2 V = s 3

7. CUBOID A hexahedron that has 6 rectangular faces. Has 12 edges but not necessarily of the same length. Surface Area = 2lb + 2bh + 2hl Volume = lbh l b h

8. Cones and Cylinders A cone has a circular or elliptical base and an apex point. A cylinder has a circular or elliptical base, & a circular or elliptical top that is congruent to the base & that lies in a plane parallel to the base. Right circular cone Frustum of Right circular cone Slant circular cone Right circular cylinder Slant circular cylinder

9. The Right Circular Cone Has circular base Has an apex point that lies on a line perpendicular to the plane of the base. S.A. = Π rs, where s = √(r 2 + h 2 ) = Π r √(r 2 + h 2 ) S.A. = Π r 2 + Π rs = Π r 2 + Π r√(r 2 + h 2 ) V = Π r 2 h/3 S LATERAL AREA SURFACE AREA OF THE CONE, INCLUDING THE BASE

10. Frustum of Right Circular Cone It is when a right circular cone was truncated by a plane parallel to the base. S.A. = Π (r 2 + r 2 ) √[h 2 + (r 2 – r 1 ) 2 ] + Π (r 1 2 + r 2 2 ), where s = √[h 2 + (r2 – r1) 2 ], then = Π s(r 2 + r 2 ) + Π (r 1 2 + r 2 2 ) S.A. = Π (r 1 + r 2 ) √[h 2 + (r 2 – r 1 ) 2 ] where s = √[h 2 + (r2 – r1) 2 ], then = Π s(r 1 + r 2 ) V = Π h( r 1 2 +r 1 r 2 + r 2 2 )/3 S.A. INCLUDING THE TOP & THE BASE S.A. EXCLUDING THE TOP & THE BASE

11. The Slant Circular Cone Has circular base Has an apex point that does not pass through the center of the base V = Π r 2 h/3 r h

12. The Right Circular Cylinder Has circular base & circular top. The base & the top lie in a parallel planes S.A. = 2 Π rh + 2 Π r 2 or = 2 Π r (h + r) S.A. = 2 Π rh V = Π r 2 h S.A. INCLUDING THE BASE S.A. EXCLUDING THE BASE

13. The Slant Circular Cylinder It has circular base and circular top The base & the top lie in parallel planes V = Π r 2 h r h

14. The Sphere These are geometric solids with curve spaces throughout. Surface Area: A = 4 Π r 2 Volume: V = 4 Π r 3 /3 r

15. THANK YOU