T1.4 Volume of Cylinder (W5M3) PDF

TOPIC 1.4. Volume of Cylinders, Cones, and Spheres LC1.8. explain inductively the volume of a cylinder using the area of a circle, leading to the identification of the formula. LC1.9. find the volume of a cylinder. LC1.10. solve problems involving the volumes of cylinders.  Th...

TOPIC 1.4. Volume of Cylinders, Cones, and Spheres LC1.8. explain inductively the volume of a cylinder using the area of a circle, leading to the identification of the formula. LC1.9. find the volume of a cylinder. LC1.10. solve problems involving the volumes of cylinders.  Three dimensional figures with length, width and height. R__________ CU _B__ E P____ C_______ CO __N_ E SP_H __E_ R_E P Y_ R _A__ M _I D _ P _R _I S_ M _  – Vertex – point / corner – Face – flat surface – Edge – – Base – line segment face where the figure rests.  Solid Figures made up Solid Figures formed with of polygonal faces. curved plane figures. All edges are straight line segments! Determine if the given figure is a polyhedron or non-polyhedron. Raise your hand if you want to answer. Answer page 163, Exercise A page 164, Exercise B page 163, Exercise A page 164, Exercise B Pyramid Cylinder Rectangular Prism Cone Sphere ‘Volume’ is a mathematical quantity that shows the amount of space occupied by an object, solid figure or a closed surface. The unit of volume is in cubic units such as m3, cm3, and in3 Focus on the short clip below: The volume of the rectangular prism in this clip is 24 cm3 because to fill in the figure, it requires 24 copies of a 1 × 1 × 1 cm cube. Ideally, to get the ‘volume’ you can just count the number of cubes that can fit inside the given solid figure. But how about those solid figures with circular parts; the non-polyhedrons?  Following the previous pattern; To determine the Volume of this cylinder, we need to solve for the AREA of the BASE and multiply it by its Height. But the base here is Circle! To find the Volume of What is the formula for Rectangular Prism, we use the formula: L x W x H the AREA of Circle? A = πr2 Multiply it by Height. Or simply get the AREA of the BASE (L x W) then Volume = πr2h multiply it by its Height  Volume of Cylinder = πr2h height (pi) π → ~ 3.14 r → radius h → height radius Example Volume of Cylinder = πr2h Determine the volume V = πr2h of the given figure: V= (3.14)(3)2 (10) V= (3.14)(9) (10) 10 cm V= 282.6 cm3 3 cm Example Volume of Cylinder = πr2h Determine the volume V = πr2h of the given figure: V= (3.14)(4)2 (11.5) V= (3.14)(16) (11.5) 4 cm V= 577.76 cm3 11.5 cm Example Volume of Cylinder = πr2h Determine the volume V = πr2h of the given figure: V= (3.14)(9)2 (5) 18 m 5m V= (3.14)(81) (5) V= 1271.7 m3 Radius is half of diameter r=9m Example Volume of Cylinder = πr2h A 12-inch pizza has a V = πr2h thickness of 0.7 inches. What is the V= (3.14)(6)2 (0.7) volume of this pizza? V= (3.14)(36) (0.7) 12 in V= 79.13 in3 0.7 in Exercise 1: Solve for the volume of each cylinder. Show your complete solution. V= πr2h V= (3.14)(2)2 (2) → V= (3.14)(4)(2) V= 25.12 m3 V= πr2h V= (3.14)(2)2 (10) → V= (3.14)(4)(10) V= 125.6 cm3 V= πr2h V= (3.14)(4)2 (4) → V= (3.14)(16)(4) V= 200.96 cm3 V= πr2h V= (3.14)(7)2 (30) → V= (3.14)(49)(30) V= 4615.8 cm3