thaash

thas226 = = = = =Surface Area and Volume Formulas=

__The surface area "S" and volume "V" of a right rectangular prism with length L, width W, and height H are;__

V = lwh** l = 4cm w = 5cm h = 2cm
 * SA = 2lw + 2lh + 2wh

SA = 2(4x5)+2(4x2)+2(5x2) SA = 76cm²
 * EX**.

V = 4x5x2 V = 40cm³

=Surface Area and Volume of Prisms=


 * //Altitude-//**upward distance or hieght.
 * //Height-//**Lenght of the altitude.



__Surface Area of a Right Prism__

S= L+2B //or you can use// S= hp+2B

__Volume Of A Prism__

V=Bh

__Cavalieri'e Principle__

If the cross section of two solids that have equal heights formed by the plane parallel to the bases of solids have equal areas then the two solids have equal volumes.

[|cavalieri's principle]

=Surface Are and Volume of Pyramids=


 * //Pyramid-//** a polyhedron with a base
 * //Base-//** the bottome of a pyramid
 * //Lateral Faces-//** A triangle that share single vertex
 * //Vertex of a Pyramid//**-Lateral faces are triangles that share a single vertex
 * //Base Edge-//** the edge of the bottom
 * //Lateral Edge-//** the edge of the lateral
 * //Altitude-//**the height of the pyramid
 * //Height-//** the altitude
 * //Slant Height-//** the altitude of the slant on the pyramid





__Surface Area of a Regular Pyramid__

S**=**L+B //or you can use// S1/2lp+B

__Volume of a pyramid__

V=1/3Bh

=Surface Area and Volume of Cylinders=

//**Bases-**//The faces formed by the translated region and its lateral faces bases and is perpendicular to both planes
 * //Cylinder-//** A solid with a circular region and its translated image on a parallel plane
 * //Lateral Surface-//**Connect the circles
 * //Altitude-//**Segment that has end points in the planes containing the
 * //Height-//**Length of altitude
 * //Axis-//**A segment joining the centers of the two bases
 * //Right Cylinder-//**Axis is perpendicular to the bases
 * //Oblique Cylinder-//**Axis not perpendicular to the bases

__Surface Area of a cylinder__ S=L+2B or S=2rh²+2r²

__Volume of a cylinder__ V=Bh or V=r²h

r = 4ft h = 10ft

SA = 24x10 + 24² SA = 351.68ft²
 * EX.**

V = 4²10 V = 502.4 ft³

=Surface Area and the Volume of a cone=

//**Vertex-**//single point not in the plane of the base //**Altitude-**//Segment from the vertex to the plane of the base
 * //Cone-//** 3 dimensional figure with a circlar base
 * //Base-//** Circular
 * //Lateral faces-//**remaininge faces, which are quadrilaterals
 * //Height-//**Lenght of altitude
 * //Right cone-//**Altitude initersects the center of the base a cone
 * //Oblique cone-//**If the altitude does not intersect the center of the base of a cone
 * //Slant Height of a cone-//**Length of the altitude of the lateral face



= = ==

__Surface Area of a right cone__ S=L+B //or you can use// S=//π// rl + //π// r²

__Volume__ V=1/3Bh //or you can use// V=1/3//π// r² h

r = 10in l = 7in h = 4in
 * EX.**

SA = 10x7 + 10² SA = 533.8in²

V = 1/310²4 V = 418.67in³

=Surface Area and Volume of Spheres= = = = = = =
 * //Sphere-

Annulus-//**

__Surface Area Of A Sphere__ S =4//π// r²

__Volume Of A Sphere__ V=4/3//π// r³

r = 9yd
 * EX.**

SA = 49² SA = 1017.36yd²

V = 4/39³ V = 3052.08yd³