- 1. By Sri.Siddalingeshwara BP M.Sc, B.Ed, (P.hd) SURFACE AREAS AND VOLUMES Chapter-13 For Class-X
- 2. Content: 1.Introduction Plane and solid figures. Definition of surface area and volume Finding the Surface area and volume of a solid figure 2.Surface Areas of a combination of solids 3.Volume of a combination of solids 4. Conversion of solid from one shape to another 5. Frustum of cone
- 3. 1.INTRODUCTION: *. From class IX, you are familiar with some of the cuboid, cube, cone, cylinder and sphere. As shown in the figure. *And also known about the finding the surface areas and volumes of the above. • Generally The above geometrical figures known as solid figures • Why they called solid figures? • And what is the difference between plane and solid geometrical figures? Cuboid
- 7. Finding the Surface area and volume 1. Finding the Surface area and Volume of Cuboid
- 8. Note: 1.The total surface area of a solid is the sum of the areas of all of the faces or surfaces that enclose the solid. The faces include the tops and bottoms (bases) and the remaining surfaces. 2.The lateral surface area of a solid is the surface area of the solid without the bases. for a cube, the lateral surface area would be the area of four sides. 3. The Curved surface area of an object is the area of all the curved surfaces in an object. For right circular cylinder the surface joining the two bases of right circular cylinder is called its curved surface Cylinder Cube
- 9. 2. Finding the surface area and volume of cube: 3. Finding the surface area and volume of cylinder: it consist of two circular ba equal area in parallel planes, that are connected by a lateral surfaces that intersects the Of the bases.
- 10. 4. Finding the surface area and volume of the cone: (l) (h) (r) 5. Finding the surface area and volume of the sphere: Slant height= 𝒓𝟐 + 𝒉𝟐
- 11. Volume of the sphere:
- 12. Curved /Lateral surface area of solids
- 13. In this chapter will discusses about the combinations of solid figures and Surface areas, Volume and Lateral surface areas or Curved surface areas of the solid figures . For example: In the above example, Truck with a container on its back carrying oil or water from one place to another place It is in the shape of combination of solid figures. i.e Cylinder with two hemispheres as it ends.
- 14. 2.Surface Areas of a combination of solids: A composite solid is a solid made up of common geometric solids The total surface area of a combined solid is the sum of the total surface areas of the individual solids that make up the combined solid, excluding the overlapping parts from each figure. Whereas the volume of a combined solid is the sum of the volumes of the individual solids that make up the combined solid. .
- 15. Example 1: let us consider truck as shown below In the above example, Truck with a container on its back carrying oil or water from one place to another place It is in the shape of combination of solid figures. i.e Cylinder with two hemispheres as it ends. So, The total surface area of the new solid is the sum of the curved surface areas of each of the individual parts. This gives TSA of new solid = CSA of one hemisphere + CSA of cylinder + CSA of the other hemisphere Where: TSA = “Total surface area” CSA = “ Curved surface area”
- 16. • Example 2: Hemisphere and a cone Find the surface area of the toy? It’s a combination of solids . That is cone and hemisphere the combine to form a Toy. As shown in the diagram. it can be calculated by Total area of the Toy= CSA of hemisphere + CSA of cone
- 17. 3.Volume of a combination of solids: Volume is a physical quantity that measures the space occupied by a solid. It is measured in cubic units. The volume of a combination of solids given by adding up the volumes of each individual solid - in the combination of solids. For example, in a figure made up of a hemisphere and a cone (like a top), the sum of the volumes of each solid gives us the volume of the combination of solids.
- 18. 4. Conversion of solid from one shape to another: When you convert one solid shape to another, it forms the other solid of same ratio. its volume remains the same, no matter how different the new shape is. In fact, If you melt one big cylindrical candle to 5 small cylindrical candles, the sum of the volumes of the smaller candles is equal to the volume of the bigger candle. Cut a watermelon into slices, they are converting a solid shape into other solid shapes. Regardless of the size and shape of the slices, there is one fact that holds true of the whole process. The volume of all the slices together exactly equals the volume of the original watermelon. Convert a solid of a given shape to a solid of another shape, the surface area usually changes. However, the volume is preserved.
- 19. Candles are generally in the form of cylinder. And some candles shaped like an animal. How They are made? If you want a candle any special shape, you have to heat the wax in a metal container till it becomes completely liquid . Then you will have to pour it into another container which has the special Shape that you want. In a figure, From cylinder candle into to rabbit shaped candle by melting the wax. here, The volume of the new candle will be the same as the volume of the earlier candle.
- 20. 1. A cylindrical pencil sharpened at one edge is the combination of (A) a cone and a cylinder (B) frustum of a cone and a cylinder (C) a hemisphere and a cylinder (D) two cylinders. Answer: (A) Explanation: The shape of a sharpened pencil is: 2. During conversion of a solid from one shape to another, the volume of the new shape will (A) increase (B) decrease (C) remain unaltered (D) be doubled Answer: (C) Explanation: During conversion of one solid shape to another, the volume of the new shape will remain unaltered MCQ type:
- 21. 3. A right circular cylinder of radius r cm and height h cm (h>2r) just encloses a sphere of diameter (A) r cm (B) 2r cm (C) h cm (D) 2h cm Answer: (B) Explanation: Because the sphere is enclosed inside the cylinder, therefore the diameter of sphere is equal to the diameter of cylinder which is 2r cm 4. If two solid hemispheres of same base radii r, are joined together along their bases, then curved surface area of this new solid is (A) 4πr2 (B) 6πr2 (C) 3πr2 (D) 8πr2 Answer: (A) Explanation: Because curved surface area of a hemisphere is and here we join two solid hemispheres along their bases of radii r, from which we get a solid sphere. Hence the curved surface area of new solid = 2πr2 + 2πr2 = 4πr2
- 22. 5. A solid cylinder of radius r and height h is placed over other cylinder of same height and radius. The total surface area of the shape so formed is (A) 4πrh + 4πr2 (B) 4πrh − 4πr2 (C) 4πrh + 2πr2 (D) 4πrh − 2πr2 Answer: (C) Explanation: Since the total surface area of cylinder of radius r and height h = 2πrh + 2πr2. When one cylinder is placed over the other cylinder of same height and radius, Then height of new cylinder = 2h And radius of the new cylinder = r Therefore total surface area of new cylinder = 2πr (2h) + 2πr2 = 4πrh + 2πr2
- 23. 6.A medicine-capsule is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends. The length of entire capsule is 2 cm. The capacity of the capsule is (A) 0.36 cm3 (B) 0.35 cm3 (C) 0.34 cm3 (D) 0.33 cm3 Answer: (A) Explanation: Since diameter of the cylinder = diameter of the hemisphere = 0.5cm Radius of cylinder r = radius of hemisphere r = 0.5/2 = 0.25 cm Observe the figure,
- 24. 7.Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is (A) 4 cm (B) 3 cm (C) 2 cm (D) 6 cm Answer: (C) Explanation: Therefore diameter of each solid sphere = 2cm
- 25. 8.Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is: (A) 3 : 4 (B) 4 : 3 (C) 9 : 16 (D) 16 : 9 Answer: (D) Explanation: According to question, Therefore ratio of surface area is:
- 26. THANK YOU References: 1 NCERT Text book. 2. Google source.