Surface Area and Volume Surface Area and Volume

PRESENTED BYSanjay SahuSandeepSanjay KabirSatyendra vermaShubham guptaShubham PrajapatiSohan lal Riuraj

Straight-Edged ObjectsStraight-Edged Objects Solids with straight Solids with straight

edges, flat faces edges, flat faces (facets), each of which (facets), each of which is a plane polygon.is a plane polygon.

Rectangular Rectangular PyramidPyramid

CubeCube CUBOIDCUBOID

Rectangular PyramidRectangular Pyramid Has rectangular base & 4 Has rectangular base & 4

slanted faces.slanted faces. If the base is a square, & If the base is a square, &

if the apex lies directly if the apex lies directly above a point at the above a point at the center of the base, then it center of the base, then it is ais a symmetrical symmetrical square pyramidsquare pyramid..

S.A. = t2 + 2t √(s2 – t2/4)

V = Ah/3

s = slant height

t = edge of the base

The CubeThe Cube It is a regular It is a regular

hexahedronhexahedron Has 12 edges & 6 Has 12 edges & 6

facesfaces

S.A. = 6s2

V = s3

CUBOIDCUBOID A hexahedron that A hexahedron that

has 6 rectangular has 6 rectangular faces.faces.

Has 12 edges but not Has 12 edges but not necessarily of the necessarily of the same length.same length.

S.A. = 2lb + 2bh + 2hl

V = lbh

l

bh

Cones and CylindersCones and Cylinders A cone has a circular or A cone has a circular or

elliptical base and an elliptical base and an apex point.apex point.

A cylinder has a A cylinder has a circular or elliptical circular or elliptical base, & a circular or base, & a circular or elliptical top that is elliptical top that is congruent to the base congruent to the base & that lies in a plane & that lies in a plane parallel to the base.parallel to the base.

Right circular coneRight circular cone Frustum of Right circular Frustum of Right circular

conecone Slant circular coneSlant circular cone Right circular cylinderRight circular cylinder Slant circular cylinderSlant circular cylinder

The Right Circular ConeThe Right Circular Cone Has circular baseHas circular base Has an apex point Has an apex point

that lies on a line that lies on a line perpendicular to the perpendicular to the plane of the base.plane of the base.

S.A. = Πrs, where s = √(r2 + h2)

= Πr √(r2 + h2)

S.A. = Πr2 + Πrs

= Πr2 + Πr√(r2 + h2) V = Πr2 h/3

S

LATERAL AREA

SURFACE AREA OF THE CONE, INCLUDING THE BASE

Frustum of Right Circular ConeFrustum of Right Circular Cone It is when a right It is when a right

circular cone was circular cone was truncated by a plane truncated by a plane parallel to the base.parallel to the base.

S.A. = Π(r2 + r2) √[h2 + (r2 – r1)2] + Π(r1

2 + r22),

where s = √[h2 + (r2 – r1)2], then

= Πs(r2 + r2) + Π (r12 + r2

2)

S.A. = Π(r1 + r2) √[h2 + (r2 – r1)2]

where s = √[h2 + (r2 – r1)2], then

= Πs(r1 + r2) V = Πh( r12 +r1r2 + r2

2)/3

S.A. INCLUDING THE TOP & THE BASE

S.A. EXCLUDING THE TOP & THE BASE

The Slant Circular ConeThe Slant Circular Cone Has circular baseHas circular base Has an apex point Has an apex point

that does not pass that does not pass through the center of through the center of the basethe base

V = Πr2 h/3

r

h

The Right Circular CylinderThe Right Circular Cylinder Has circular base & Has circular base &

circular top.circular top. The base & the top lie The base & the top lie

in a parallel planesin a parallel planes

S.A. = 2Πrh + 2Πr2 or

= 2Πr (h + r)

S.A. = 2Πrh

V = Πr2 h

S.A. INCLUDING THE BASES.A. EXCLUDING THE BASE

The Slant Circular CylinderThe Slant Circular Cylinder

It has circular base It has circular base and circular topand circular top

The base & the top lie The base & the top lie in parallel planesin parallel planes

V = Πr2 h

r

h

SphereSphere These are geometric solids with curve spaces These are geometric solids with curve spaces

throughout.throughout.

Sphere

The SphereThe Sphere

Surface Area:Surface Area:

A = 4A = 4ΠΠrr22

Volume: Volume:

V = 4V = 4ΠΠrr33 /3 /3r

THANK YOUTHANK YOU