Area and Volume

SURFACE AREAS

AND VOLUMES

ContentsSurface areas and volumes of :-

Cube Cuboid Cylinder Cone Sphere and hemisphere

Cube DEFINATION:-A cuboid whose length ,breadth,

height are equal is called a cube. SOLID CUBE:-A solid cube is the part of the

space enclosed by six faces of the cube.

Parts of cube A cube is a region of space formed

by six identical square faces joined along their edges. Three edges join at each corner to form a vertex.

SURFACE AREA OF A CUBE

SURFACE AREA OF CUBE: Since all six faces of a cube are squares of the same size i.e. For a cube we have l=b=h. Thus, if l cm is the length of edge or side or a cube , then

Therefore, surface area of a cube=6(a)square.

What is a Cuboid ?..A solid which has six rectangular faces at right angles to each other.

Surface area of the CuboidSurface Area without the Top = 2 (bh + hl)

+ lb .Surface Area without Top & Base = 2 (bh +

hl). Total Surface Area =2 (lb + bh + hl).

Lets Memorize !-T.S.A of a cube = 6a2.-Lateral surface area of cube= 4(edge)sq. -Volume of cube= (edge) cubic .

-T.S.A of a cuboid = 2(lb+bh+lh).-L.S.A of a cuboid = 2 (l + b) h.-Volume of the cuboid = lbh .

Cylinder 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.

Surface area of Cylinder

TSA of a cylinder = area of the base + area of top + CSA of the cylinder

= ∏r2 + ∏r2 + 2∏rh

= 2∏r2 + 2∏rh = 2∏r(r + h) Where, r is the radius h is the height of the

cylinder

Volume of the cylinder Volume of the cylinder = area of the

base x height = r2 x h = ∏r2h Volume of hollow cylinder = ∏(R2 - r2)

h Where, r is the radius and h is the

height

Introduction to cone

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

Surface area of a Cone TOTAL SURFACE AREA =curved surface area

+area of the base = ∏rl+ ∏r2 + = ∏r(r+l)

Curved surface area of cone =area of sector

=1/2 *l *(2 ∏r) = ∏r l

Introduction to Sphere & Hemi-sphere1.A sphere is a perfectly round geometrical object in three-dimensional space.

2. Hemisphere refers to the equal halves of the sphere and can also be called the 3d design for a semi-circle.

Surface Area of Sphere When we talk about painting or polishing the surface it is related to the surface area. Surface-Area (TSA) = 4∏r2

Where, ‘r’ is the radius from the center to surface.

Volume of Sphere When we talk about the air in the

solid or want to count the no. of small object from the bigger one then it is related to the volume.

Volume of the sphere = 4/3∏r3

Where, r is the radius.

Surface Areas of Hemisphere

TSA of hemisphere = 3∏r2 CSA of hemisphere = 2∏r2

Where, ‘r’ is the radius.

Volume of Hemisphere

Volume of the Hemisphere = 2/3∏r3

Where, r is the radius.

Thank You !

By-Mayand SinghClass-9th “C”