SURFACE AREAS

AND VOLUMES

CONTENTSSURFACE AREAS AND VOLUMES OF :-CUBOID CUBECYLINDERCONESPHERE

CUBOIDSURFACE AREA

Area of Rectangle 1 = (lxh) +Area of Rectangle 2 = (lxh) +Area of Rectangle 3 = (lxb) +Area of Rectangle 4 = (lxb) +Area of Rectangle 5 = (bxh) +Area of Rectangle 6 = (bxh) + = 2(lxb) + 2(bxh) + 2(lxh) = 2(lb + bh + lh)

VOLUME

CUBE

Area of square 1 = a x aArea of square 2 = a x aArea of square 3 = a x aArea of square 4 = a x aArea of square 5 = a x aArea of square 6 = a x aSurface Area = Area of all 6 faces = 6a2

SURFACE AREA

VOLUME

CYLINDER

Circumference of a circle = 2πrArea covered by a circle = (2πr) x (h) = 2πrh

CURVED SURFACE AREA

TOTAL SURFACE AREA

Area of curved surface + Area or two circles

= (2πr) + (h) + 2πr2

= 2πr (r + h)

VOLUME

CONECURVED SURFACE AREA

After cutting the cone,Curved Surface area = Area of sectorTherefore, Curved surface area =1/2 (l) (2πr) = πrl

TOTAL SURFACE AREA

Total Surface Area = Curved Surface Area +

Area of bottom Circle

= πrl + πr2

= πr (l + r)

VOLUME

SPHERE

The surface area of a sphere with radius r = 4πr2

SURFACE AREA

The curved surface area of a hemisphere with radius r = 2πr2 and the total surface area = 3πr2

VOLUMEIf we make a cone having radius and height equal to the radius of sphere. Then a water filled cone can fill the sphere in 4 times.

rr

V1

r

V=1/3 πr2h

If h = r then

V=1/3 πr3

V1 = 4V = 4(1/3 πr3)

V1= 4/3 πr3