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1. SURFACE AREAS AND VOLUMES

2. 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.

3. 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)

4. SURFACE AREA OF CUBE
A 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

5. 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
Curved Surface Area of Cylinder =
= perimeter of the base of the
cylinder x h
= 2πr x h
2πrh

6. 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)

7. SURFACE AREA OF A SPHERE
A 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

8. 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 ²
Curved Surface Area of Hemisphere
= 2 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.
Total Surface Area of Hemisphere = 3 πr ²

9. volumes

10. Is the amount of space occupied by any
3-dimensional object.
Volume = base area x height
= 1cm2 x 1cm
= 1cm2Volume = base area x
height

11. Cuboid
Side 2
Back
Top
Bottom
Side 1
Front
Length (L)
Height (H)
Breadth (B)

12. The Net
B
L
H
B
H
B
H
B
L
L
L
L
H
B
H
B
H

13. Total surface Area
H L
H
B B
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
L
B
H
L
L
L
L
H
H

15. Cube
L
L
• Volume = Base area x height
= L x L x L
= L3
• Total surface area = 2LxL + 2LxL + 2LxL
= 6L2
L

16. Cube L3 6L2
2(LxB + BxH +
LxB)
LxB
Cuboid
Sample
net
Total
surface
area
Name Figure Volume

17. 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

18. 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

19. 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

20. Thank You
Done By –
Mohammed Hafeez &
IX std A sec