Surface Area, Lateral Area, and Volume Formulas

1 SurfaceAreaLateralAreaVolumeFormulas area , Lateral area , and Volume FormulasIn the table shown Bis the area of the base, Pis the perimeter of the base, his the height of the object, lis the slant height of the object, ris the radius of the base if the base is a circle, Cis the circumference of the base if it is a circle, Sis the Surface area of the object, Lis the Lateral area of the object, and Vis the Volume of the AreaSurface AreaVolumeRight PrismL=PhS=2B+LorS=2B+PhV=BhRight CylinderL=Chor L=2 rhS=2B+LorS=2B+Chor S=2 r2+2 rhV=Bhor V= r2hRegular PyramidL=12 PlS=B+LorS=B+12 PlV=13 BhRight ConeL=12 ClOrL= rlS=B+LorS=B+ rlorS= r2+ rlV=13 Bhor V=13 r2hSphereS=4 r2V=43 r3 Right PrismLateral area of a right prism:L=Phwhere L is the Lateral area and Ph is the product of the perimeter of one of the bases and the height of the prism.

2 Lateral area is the Surface area minus the area of the bases. The Lateral area consists of only the area of the Lateral faces of a area of a right prism:S=2B+LorS=2B+Phwhere S is the total Surface area , 2B is twice the area of one of the bases. The Lateral area isLorPhand is the product of the perimeter of one of the bases and the height of the of a prism: V=Bhwhere Bis the area of the base andhis the CylinderLateral area of a right cylinder:L=Chwhere L is the Lateral area and Ch is the product of the circumference of one of the bases and the height of the cylinder. Lateral area is the Surface area minus the area of the bases. Think of a cylinder as a soup can. The Lateral area is the label. If the label was removed and laid flat it would be a rectangle.

3 The height of the rectangle is the same as the height of the cylinder and the length of the rectangle would be the circumference of the circle that is the base of the 's Notes page 1 of 2surfaceAreaLateralAreaVolumeFormulas area of a right cylinder:S=2B+LorS=2B+Chor S=2 r2+2 rhwhere S is the total Surface area , 2B is twice the area of one of the bases (the area of the circle 2 r2that is the base in the case of a cylinder) andLor Chis the Lateral the product of the circumference of one of the circles and h the height of the of a cylinder:V=Bhor V= r2h where Bis the area of the base (which is a circle and thus gives the second formula ) and his the height of the PyramidLateral area of a regular pyramid:L=12 PlL is the Lateral area , P is the perimeter of the base and l is the slant height of the area of a regular pyramid:S=B+LorS=B+12 PlS is the Surface area , B is the area of the base,Lis the Lateral area , P is the perimeter of the base and l is the slant height of the of a regular pyramid: V=13 Bhwhere Bis the area of the base and his the height of the ConeLateral area of a right cone:L=12 ClorL= rl In the first formula Cis the circumference of the circle that is the base and lis the slant height of the cone.

4 When the circumference is divided by 2 you get rwhich is half the circumference which results in the second area of a right cone:S=B+LorS=B+ rlor S= r2+ is the Surface area , B is the area of the base,Land rl are the Lateral area of the of a right cone: V=13Bh or V=13 r2h where Bis the area of the base and his the height of the area of a sphere:S=4 r2 Where Sis the Surface area of a sphere and ris the of a sphere:V=43 r3 Where Vis the Volume and ris the 's Notes page 2 of 2