3 d figures, its surface areas and volumes

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A cuboid is a 3-d shape in which all angles are right angles, and opposite faces are equal.

Lateral Surface area

The lateral surface area of a cuboid is 2h(l+b), i.e. ,2 x height x sum of length and breadth

Surface area

The surface area of a cuboid is 2(lb+bh+hl) , i.e. , 2 x (length x breadth + breadth x height +

height x length)

Volume of cuboid is lbh , i.e. , length x breadth x height

Lateral Surface area

The lateral surface area of cube is 4a2

Surface areaThe surface area of cube is 6a2

Volume of cube is a2

A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the

points at a fixed distance from a given line segment, the axis of the cylinder. The solid enclosed by this surface and by two planes

perpendicular to the axis is also called a cylinder.

Lateral surface area

The lateral surface area of cylinder is 2πrh

Surface areaThe surface area of cylinder is 2πr(r+h)

Volume of cylinder is πr²h

A cone is a 3-dimensional geometric shape that tapers smoothly from a base (usually flat and circular) to a point called the apex or vertex.

In common usage in elementary geometry, cones are assumed to

be right circular, where right means that the axis passes through the centre of the base

(suitably defined) at right angles to its plane, and circular means that the base is

a circle.

Lateral surface area

Lateral surface area of cone is πrl

Surface area Surface area of cone is πr(l+r)

Volume of cone is 1/3 πr² h

A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle, which is in two

dimensions, a sphere is the set of points which are all the same distance r from a given point in space. This distance r is known as the radius of

the sphere, and the given point is known as the center of the sphere. The maximum

straight distance through the sphere is known as the diameter. It passes through the center

and is thus twice the radius.

Total surface area of sphere is 4πr²

The volume of a sphere is 4/3πr3

A sphere is divided into two equal "hemispheres" by any plane that passes through its center. If

two intersecting planes pass through its center, then they will subdivide the sphere into four lunesor bi-angles, the vertices of which all coincide with the antipodal points lying on the

line of intersection of the planes.

Curved surface area

The curved surface area of Hemisphere is 2πr2

Surface area The total surface area of hemisphere is 3πr2

The volume of hemisphere is 2/3πr3