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# Formula for Surface Area and Volume

Surface Area and Volume Formula:

The surface area of a solid  geometric figure is the sum of the area of all surfaces of a figure. Volume of the figure gives the quantity of space occupied.

Surface area and volume formula of the geometric figure are given below

 Sl.No Figure Formula for surface area Formula for volume 1 Rectangular Prism SA = 2ab+2bc+2ca  sq. units where a, b,c are the sides of the cube. V = abc  cubic units 2 Cylinder SA = 2πrh  sq. units  TSA =  2πr(h+r)  sq. units   r =radius of the cylinder  h – height of the cylinder V = πr2h   cubic units 3 Cube SA = 6a2  sq. units   a = sides of the cube V = a3    cubic units 4 Sphere SA = 4πr2    sq. units  r = radius of the sphere V = $\frac{4}{3}$ πr3   cubic units 5 Ellipsoid SA = $4\pi \left [ \frac{a^pb^p+a^pc^p+b^pc^p}{3} \right ]^{\frac{1}{p}}$ p = 1.6075 a, b, c are semi axis of ellipsoid V = $\frac{4}{3}$ π r1,r2,r3  cubic units 6 Cone CSA = πrl sq. units V = $\frac{1}{3}$ πr2h   cubic units 7 Pyramid SA = a + $\frac{1}{2}$ *p*l   p = perimeter of pyramid   l = slant height   a= area of the base of the pyramid V = $\frac{1}{3}$ *a*h  cubic units 8 Torus SA =  π2 * (R2 - r2)   R: Outer Radius  r: Inner Radius V = $\frac{1}{4}$ π3 (r1 + r2) (r1 - r2)2  cubic units 9 Hemisphere CSA = 2πr2   TSA = 3πr2  r = radius V = $\frac{2}{3}$ πr3   cubic units 10 Triangle SA = $\sqrt{s(s-a)(s-b)(s-c)}$ where s is the perimeter of the triangle a, b, c are the sides of the triangle 11 Rectangle A = l*w L = length w = width 12 Triangle A = $\frac{1}{2}$ bh b = base  h = height 13 Trapezoid A = $\frac{1}{2}$ h (b1+b2) 14 Parallelogram A = bh 15 Circle A = πr2   r = radius

Question:

Answers:For a rectangular prism volume the formula is L x W x H, and the surface area is 2( LW + LH + WH). For prisms the volume formula is Area of the base times the height. The surface area is 2 X Area of base + # of sides X Width X Height. For pyramids the volume is 1/3 Base times height. Surface area is area of base + # of sides X 1/2 Width times slant height. A cube's volume is L^3, and its area is 6 times (L^2) A sphere is 4/3 pi r^3 for volume and 4/3 pi r^2 for surface I suggest you check these in a good geometry book, and find the rest.

Question:Forgot to bring my algebra II book home with me!

Answers:V = (4/3)*pi*r^3 A = 4*pi*r^2 You could have found these easily by using google.

Question:basically i need all the formulae of finding the surface areas and volumes of diff 3d shapes...eg. cuboid,pyramid,cylinder,sphere,diff prisms,cube,cone etc