Surface areas and volumes

CONTENTS

CUBE

CUBOID

CYLINDER

CONE

SPHERE

HEMISPHERE

FRUSTUM

• An object which looks like solid box-shaped that has six identical square faces.

• A cube has 6 equal and plane surfaces. All the faces of a cube are square in shape.

• In a cube there are 6 plane surfaces. There are 8 vertices and 12 edges.

• Two adjoining plane – surfaces meet at an edge. There are 12 edges in a cube and all the 12 edges are equal in length. These edges are straight edges.

• The meeting point of two edges is called a vertex. In a cube there are 8 such vertices.

SURFACE AREA OF CUBE

TOTAL SURFACE AREA OF CUBE- 6(SIDE)²

LATERAL SURFACE AREA OF CUBE-4(SIDE)²

VOLUME OF CUBE

VOLUME OF CUBE-(SIDE)³

• The cuboid has 6 rectangular faces. The opposite rectangular plane surfaces are identical (equal in all respects). It has 8 vertices and 12 edges.

• In a cuboid there are 6 rectangular plane surfaces. There are 8 vertices and 12 edges.

• A cube is also a cuboid having all its 6 faces equal and square. Thus, a cube has all the six faces identical, whereas a cuboid has the opposite faces identical.

SURFACE AREA OF CUBOID

TOTAL SURFACE AREA OF CUBOID =

2(lb+BH +lh)

LATERAL SURFACE OF CUBOID:

2(l+b)h

VOLUME OF CUBOID

VOLUME OF CUBOID –L*B*H

• A cylinder stands on a circular plane surface having circular plane surfaces on its top and bottom. Thus a cylinder has two circular plane surfaces, one at its base and another at its top. It has a curved surface in the middle.

• It has two edges, at which the two plane surfaces meet with the curved surface. These edges are curved edges.

• In a cylinder there are 2 plane surfaces and 1 curved surface. There are 2 edges and no vertices.

• The base and top of a cylinder are of the same shape (circular) and size. Thus, both are identical.

• cylinder

SURFACE AREA OF CYLINDER

Curved surface area: 2Пrh

Total surface area: Пrh +2Пr2

=2ПR(H+R)

VOLUME OF CYLINDER

Volume of a cylinder: Пr2h

• A cone has one plane circular surface, i.e. its base and only one curved surface. In a cone there is 1 plane surface and 1 curved surface. There are 1 edge and 1 vertex.

• It has one edge which is formed by the circular plane surface meeting with the curved surface. The edge of a cone is a curved edge.

CONE

SURFACE AREA OF CONE

TOTAL SURFACE AREA OF CONE-

∏R(L+R)

LATERAL SURFACE AREA OF CONE-

∏RL

VOLUME OF CONE

VOLUME OF CONE-1/3 Пr²h

SPHERE

• The ball-like shape is called a sphere.

• In sphere there is curve surface, no edge and no vertex.

• Some of the common solid figures are explained above in brief with the labeled diagram to get the basic ideas of the solid shapes.

SPHERE

SURFACE AREA OF SPHERE

VOLUME OF SPHERE

HEMISPHERE

SURFACE AREA OF

HEMISPHERE

TOTAL SURFACE AREA OF A HEMISPHERE:

3ПR 2

CURVED SURFACE AREA OF A HEMISPHERE:

2ПR 2

VOLUME OF HEMISPHERE

VOLUME OF A CUBE:

2/3 ПR 3

FRUSTUM

SURFACE AREA OF FRUSTUM

TOTAL SURFACE AREA OF A FRUSTUM:

П(R+R)L + ПR 2 + ПR 2

=П(R+R)L + П(R 2+ R2)

CURVED SURFACE AREA OF A FRUSTUM:

П(R+R)L

VOLUME OF FRUSTUM

VOLUME OF A FRUSTUM:

1/3 ПH(R 2+R 2+RR)