3. WHAT IS A SPHERE?
A sphere is a geometrical figure that is perfectly round, 3-
dimensional and circular - like a ball.
4. WHAT IS A SPHERE?
Geometrically, a sphere is defined as the set of all points
equidistant from a single point in space.
It is a shape of biggest volume with the smallest surface area.
5. SPHEROID?
Watermelon and Earth is not exactly a sphere as it is not perfectly
round.
This are known as spheroid.
6. PROPERTY OF A SPHERE
It is perfectly symmetrical
All points on the surface are the same
distance from the center.
It has no edges or vertices (corners)
8. VOLUME OF SPHERE
Volume=
4
3
𝜋𝑟3
General Formula for Volume of sphere
R is radius
By rearranging the above formula,
you can find the radius:
Radius=
3 3𝑣
4𝜋
9. EXAMPLE
Find the volume of a sphere of radius 9.6 m, rounding your answer to two decimal
places.
V =
4
3
𝜋𝑟3
4
3
× 𝜋 × 9.63
(replace r with 9.6)
4
3
× 𝜋 × 884.736
= 3705.97 𝑚3
9.6 m
10. SURFACE AREA OF SPHERE
Surface Area = 4𝜋𝑟2
By rearranging the above formula,
you can find the radius:
Radius=
𝑎
4𝜋
11. EXAMPLE
Find the surface area of a sphere of diameter 28 cm.
Radius = ½ Diameter
Surface Area = 4𝜋𝑟2
4 × 𝜋 × 142 (28 divide by 2 and replace r with it)
= 2464 𝑐𝑚2
28 m
14. VOLUME OF HEMISPHERE
It is exactly half of the sphere so:
4
3
𝜋𝑟3
÷ 2
Volume =
2
3
𝜋𝑟3
15. EXAMPLE
Find the volume of a hemisphere, whose radius is 10 cm.
V =
2
3
𝜋𝑟3
2
3
× 𝜋 × 103 (replace r with 10)
2
3
× 𝜋 × 1000
= 2093.3 𝑚3
10 cm
16. SURFACE AREA OF HEMISPHERE
The surface area of hemisphere is equals to half of surface area of
sphere plus the area of the base (circle).
2𝜋𝑟2 + 𝜋𝑟2
Therefore Surface Area =3𝜋𝑟2
this is only if the question asked about total surface area.
17. EXAMPLE
Find the total surface area of a hemisphere, whose radius is 8 cm.
Surface Area = 3𝜋𝑟2
3 × 𝜋 × 82 (replace r with 10)
2
3
× 𝜋 × 64
= 602.88 𝑐𝑚2
10 cm
19. WHAT IS A PRISM?
A prism is a geometrical solid object with two identical ends and
flat sides.
20. CROSS SECTION
A cross section is the shape made by cutting straight across an
object.
A prism must have the same cross section all along its length.
21. NO CURVES!
A prism is a polyhedron which means all faces must be flat.
22. PARALLEL SIDES
The side faces of a prism are parallelograms.
When to ends are not parallel it is not a prism.
24. VOLUME OF PRISM
Volume = Base Area × Length
Base Area is calculated normally depends on the shape.
25. EXAMPLE
What is the volume of a prism where the base area is 25 m2 and which is 12 m
long:
Volume = Base Area × Length
𝑉𝑜𝑙𝑢𝑚𝑒 = 25 𝑥 12
= 300 𝑚3
26. SURFACE AREA OF PRISM
Surface Area = (2 x Base Area) + (Base Perimeter x Length)
27. EXAMPLE
What is the surface area of a prism where the base area is 25 m2, the base perimeter
is 24 m, and the length is 12 m:
Surface Area = (2 x Base Area) + (Base Perimeter x Length)
𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝐴𝑟𝑒𝑎 = (2 × 25) + (24 × 12)
𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝐴𝑟𝑒𝑎 = 50 𝑚2 + 288 𝑚2
= 338 𝑚2