SURFACE AREA & VOLUME EX-12.1 QUE(6 TO 9) скачать в хорошем качестве

SURFACE AREA & VOLUME EX-12.1 QUE(6 TO 9)

SURFACE AREAS AND VOLUMES – DESCRIPTION 1. Surface Area Surface area is the total area occupied by the surfaces of a 3D object. It includes the curved surface area (CSA) and total surface area (TSA) depending on whether the object has flat or curved faces. It helps us find how much material is needed to cover a solid. 2. Volume Volume is the space contained inside a 3D object. It measures how much liquid, gas, or substance a container can hold. Volume is always expressed in cubic units. 3. Surface Area of a Cube A cube has 6 equal square faces. TSA = 6a², where a is the side of the cube. It is used for finding paint, wrapping paper, or covering a cubical box. 4. Volume of a Cube The volume of a cube shows how much space is inside it. Volume = a³ Used for finding capacity of storage boxes, water tanks of cubical shape, etc. 5. Surface Area of a Cuboid A cuboid has 6 rectangular faces. TSA = 2(lb + bh + hl) It helps calculate materials for making bricks, boxes, or rooms. 6. Volume of a Cuboid The space inside a cuboid. Volume = l × b × h Useful for storage containers, rooms, and tanks. 7. Surface Area of a Cylinder A cylinder has two circular bases and a curved surface. CSA = 2πrh TSA = 2πr(r + h) Used for finding labels on cans, paint for pipes, etc. 8. Volume of a Cylinder Shows how much liquid a cylinder can store. Volume = πr²h Applied in water tanks, bottles, and pipes. 9. Surface Area and Volume of a Cone A cone has one circular base and a curved surface. CSA = πrl (l = slant height) TSA = πr(r + l) Volume = ⅓πr²h Used in ice-cream cones, funnels, traffic cones, etc. 10. Surface Area and Volume of a Sphere & Hemisphere A sphere is a perfectly round solid. Surface Area (Sphere) = 4πr² Volume (Sphere) = 4/3 πr³ A hemisphere is half of a sphere. CSA (Hemisphere) = 2πr² TSA (Hemisphere) = 3πr² Volume = 2/3 πr³