A Solid Presentation
Transcript: FIND THE SURFACE AREA OF THIS WEIRD SHAPE! VOLUME The Cylinder Area of one base x the height 36 ft cubed! (6)(6) ft. ft. By Daniella Elazar FORMULAS The area covered by the Great Pyramid can accommodate St Peter's in Rome, the cathedrals of Florence and Milan, and Westminster and St Paul's in London combined! (Pi)(Radius squared)(Height) SURFACE AREA (pi)(radius)(slant height) An ice cream cone is a cone! ft. 1/3(Pi)(radius squared)(height) LATERAL AREA: The two bases are circles (which are round and have no sides) .5(Perimeter of the base) (slant height) + area of the base) Volume of odd shape= 117.81 ft sq+36 ft. sq Volume of odd shape= 153.81 ft. sq The Pyramid The cylinder looks like a tube! When unraveled, a cylinder is a rectangle! (Super cool, I know) Its face is a [2-dimensional] rectangle 1440 sq. ft + 84.82 sq. ft= 1524.82 sq. ft.= Total surface area of the weird shape. not drawn to scale DID YOU KNOW? Next, we'll find the surface area of the cone The Cone VOLUME ft. Cylinder and Rectangular prism This is the circular base of the cone! Let's just focus on this one though VOLUME The sum of all of the areas of all of the faces of a solid together (not including the bases!) First, let's find the volume of the cylinder: V= (Pi) (radius squared) (height) V= 2.5(squared)(6)(Pi) V= 37.5(Pi) V= 117.81 ft sqaured Formulas :D V= 1/3 (Base)(Height) V= 1/3 (7x7)(10) V= 1/3 (49)(10) V= 1/3 (490) V= 169 square inches VOLUME The Prism The area of all faces added together + area of both bases added together This is what the net of a pyramid looks like FIND THE LATERAL AREA! The sum of all of the rectangular faced areas (3)(6)(pi) + (6 squared) (pi) 18 (pi) + 36 (pi) 169.65 units squared SA= .5(perimeter of the base)(slant height)+ area of base SA= .5(20x4)(26) +(20x20) SA= 1440 square ft. ft. the sum of all areas of all sides plus the area of the base of solid figures An empty paper towel roll is a cylinder! :) But the prism is named depending on what its base is LATERAL AREA Remember to always have cubic units when finding volume! 1440 sq ft.= SA of pyramid 84.82 sq. ft= SA of Cone FIND THE VOLUME! SURFACE AREA This is what the net of a cone looks like! 2(Pi)(Radius)(Height) Lateral Area EXAMPLES OF PROBLEMS INVOLVING MORE THAN ONE SOLID FIND THE VOLUME ft. 1/3(area of the base)(height) 2(pi)(5in)(7in) ft. LATERAL AREA This printed Wikipedia is a rectangular prism! SA=(Pi)(Radius)(Slant Height)+(Pi) (Radius sqaured) SA=(Pi)(3)(6)+(Pi)(3 squared) SA=(Pi)(18)+(Pi)(9) SA= 84.82 square ft. feet 2(Pi)(radius)(height)+ 2(pi)(r squared) [area of circle] FORMULAS Finally, we add the two surface areas together: FIND THE SURFACE AREA: A Solid Presentation Surface Area ft. SURFACE AREA 219.91 in squared ft. Area of the base x height .5(Perimeter of base) (slant height) Now, find the volume of the rectangular prism part! V=Area of base x Height V= (2 x 3) (6) V= (6)(6) V= 36 YAY! SURFACE AREA When the rectangular prism is unfolded, this is what it looks like! ft. It Doesn't Have to Be Circular Usually when we say Cylinder we mean a Circular Cylinder, but you can also have Elliptical Cylinders, like this one: The rectangular prism is the most used shape in the world! You see rectangular prisms every day! A prism has rectangular faces LATERAL AREA THE NET OF A CYLINDER (WHEN IT COMES UNRAVELED) LOOKS LIKE THIS! Fun Fact: three cones can fit into one cylinder feet (measurements are in feet) (pi)(radius)(slant height) + (pi)(radius squared) To find the total volume, just add the individual volumes of both shapes together! (volume of the cylinder+volume of the rectangular prism) Formulas FIND THE VOLUME OF THIS ODD SHAPE! 2(pi)(radius)(height) First, let's find the Surface Area of the pyramid (Pi)(radius)(slant height)+ (pi) (radius squared) Pretend they're connected (2x3)(6) DEFINITIONS: The measure of a space inside a solid figure (in cubic measurements!) VOLUME And Shaindy Stern
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