CK12 - Geometry

As with prisms,cylinderscan berightoroblique. The side of a right cylinderis perpendicularto its circular bases.The side of an o ...

To find the width,imaginetakinga can-likecylinderapartwith a scissors.Whenyou cut the lateralarea, you see that it is equalto th ...

Calculate. Find the area of the entirecylinder. Thus,the total surfacearea is approximately854.08squareunits SurfaceAreaof a Cyl ...

Factoringout a from the equationgives: The SurfaceAreaof a RightCylinderA right cylinderwith radius and height can be expresseda ...

Write the formulaand substitutein the valuesand solve. Example 4 Find the heightof a cylinderthat has radius cm and surfacearea ...

The volumeof eachindividualslice wouldbe givenby the productof the area of the baseand the height. Sincethe heightfor eachslice ...

Use the postulateto find the volumeof the cylinder. Write the formulafrom the postulate.Thensubstitutein the valuesand solve. Ex ...

Step 3: Subtractthe volumeof the hole from the volumeof the entirecylinder. Hereare the stepscarriedout. First,use the formulato ...

Now find the lengthof the sidesof the two holes.The widthof the entireblockis 21 cm. This is equalto: So the sidesof the squareh ...

Use the formulato find the volumeof this cylinder. Matthew’s favoritemug is a cylinderthat has a basearea of 9 squareinchesand ...

Supposeyou workfor a companythat makescylindricalwatertanks.A customerwantsa tank that measures9 metersin heightand 2 metersin ...

Find the volumeof a pyramid. Introduction A pyramidis a three-dimensionalfigurewith a singlebaseand a threeor morenon-parallel ...

We’ll call the slantheight for this problem.Usingthe PythagoreanTheorem: Now find the area of eachtriangle: As thereare triangle ...

The area of the hexagonalbaseis givenby the formulafor the area of a regularpolygon.Sinceeachside of the hexagonmeasures cm, the ...

SurfaceAreaof a RegularPyramid To get a generalformulafor the area of a regularpyramid,look at the net for this squarepyramid. T ...

Areaof a RegularPyramidThe surfacearea of a regularpyramidis where is the slantheightof the pyramidand is the perimeterof the re ...

cm. Find the surfacearea of the figure. First find the lateralarea of the figure. Now use the formulafor the area of a regularpo ...

The prismmay appearto be greaterin volume.But how can youprovethat the volumeof the prismis greater than the volumeof the pyrami ...

The reasonshouldbe obvious.At the “bottom,”both figuresstart out the same—witha squarebase.But the pyramidquicklyslantsinward,“c ...

And, sincethe volumeof a squareprismis , we can write: This can be writtenas the VolumePostulatefor pyramids. Volumeof a Pyramid ...