SURFACE AREAS AND VOLUMES

Surface Area of a Cuboid

The outer surface of a cuboid is made up of six rectangles(infact, rectangular regions, called the faces of the cuboid), whose areas can be found by multiplying length by breadth for each of them separately and then adding the six areas together.If we take the length of the cuboid as l, breadth as b and the height as h , then the figure with these dimensions would be like the shape use in the fig.

The sum of areas of six rectangles is :Area of rectangle A(=l×h)+Area of rectangle B(=l×b)+Area of rectangle C(=l×h)+Area of rectangle D(=l×b)+Area of rectangle E(=b×h)+Area of rectangle F(=b×h) = 2(l×b)+2(b×h)+2(l×h) = 2(lb+bh+hl)

This gives us: Surface Area of a Cuboid = 2(lb+bh+hl)

SURFACE AREA OF CUBEA cuboid, whose length breadth and height are all equal, is called a cube. If each edge of the cube is a, then the surface area of the cube would be : 2(a×a + a×a + a×a), i.e., 6a²

SURFACE AREA OF A RIGHT CIRCULAR CYLINDER

h

l

h

The area of the sheet gives us the curved surface area of the cylinder. Note that the length of the sheet is equal to the circumference of the circular base which is equal to 2πr. So, Curved Surface Area of a Cylinder = area of the rectangular sheet = length x breadth = perimeter of the base of the cylinder x h = 2πr x h

Curved Surface Area of Cylinder = 2πrh

If the top and the bottom of the cylinder are also to be covered, then we need two circles to do that, each of the radius r, and thus having an area of πr² each (see fig), giving us the total surface area as 2 πrh + 2 πr² = 2 πr (r+h).Where h is the height of the cylinder and r is radius.

Total Surface Area of a Cylinder = 2 πr (r+h)

SURFACE AREA OF A SPHEREA sphere is a three dimensional figure(solid figure), which is

made up of all points in the space, which lie at a constant distance called the radius, from a fixed point called the center of the sphere.The Surface area of Sphere of radius r = 4 times the area of a circle of radius r = 4 × (πr²)

Surface Area of Sphere = 4πr²

Surface Area of Hemisphere

When a Sphere is divided in two equal parts, each half is called a Hemisphere. A hemisphere has two faces, it is the curved face and the flat face(base)The curved surface area of a hemiphere is half the surface area of the sphere, which is ½ of 4πr ²Curved Surface Area of

Hemisphere = 2 πr ²

Total Surface Area of Hemisphere = 3 πr ²

Taking the two faces of a hemisphere, its surface area 2 πr ² + πr ², we get the total surface area of the hemisphere.

volumes

Volume = base area x height

= 1cm2 x 1cm

= 1cm2Volume = base area x height

Is the amount of space occupied by any 3-dimensional object.

Cuboid

Side 2

Bottom

Back

Top

Side 1Front

Length (L)Breadth (B)

Height (H)

The Net

B

L

H

B

H

B

H

B

L

L

L

L

H

B

H

B

H

Total surface Area

Total surface Area = L x H + B x H + L x H + B x H + L x B + L x B

= 2 LxB + 2BxH + 2LxH

= 2 ( LB + BH + LH )

H L

LH

L

B

HL

L

L

L

BB

H

H

H

Cube

• Volume = Base area x height= L x L x L= L3

• Total surface area = 2LxL + 2LxL + 2LxL

= 6L2

L

LL

2(LxB + BxH + LxB)

LxBCuboid

6L2L3Cube

Sample net

Total surface area

VolumeFigureName

Volume of a Cuboid

A Cuboid is a 3 dimensional shape.So to work out the volume we need to know 3 measurements

Look at this shape.There are 3 different measurements:

Height,   Width,   Length

The volume is found using the formula:Volume = Height × Width × Length

Which is usually shortened to:V = h × w × l

Or more simply:V = howl

It doesn't really matter which one is length, width or height, so long as you multiply all three together

What is the volume of this object?

Volume =4 × 5 × 10 = 200 units3

It also works out the same like this:10 × 5 × 4 = 200 units3

Thank You

Done By – Mohammed Hafeez &

IX std A sec