formula maths cass 9th

1. BASIC FORMULA
SURFACE AREAS AND VOLUME
PRESENTED BY RAKESH VERMA

2. INDEX
• CUBE
• CUBOID
• RIGHT CIRCULAR CYLINDER
• CONE
• SPHERE

3. CUBE
IF THE LENGTH OF EACH EDGE OF A CABE IS A UNITS
• VOLUME OF CUBE= a³
• TOTAL SURFACE AREA=6a²
• DIGONAL OF CUB=a 3

4. CUBOID
• Let l,b and h denote respectively
the length,breadth and height of a
cuboid then.
• Volume = lbh
• Total surface = 2(lb+bh+lh)
• Digonal of the
cuboid= 𝑙2 + 𝑏2 + ℎ²

5. CYLINDER(RIGHT CIRCULAR CYLINDER)
• For base radius ‘r’ and height ‘h’ then.
• Curved surface area=2𝜋𝑟ℎ
• Total surface area=2𝜋𝑟(h+r)
• Volume= 𝜋𝑟²ℎ

6. HELLOW CYLINDER
• Let ‘R’ and ‘r’ be the external and
internal radius of a hellow cylinder of
height ‘h’ then.
• Curved surface area=2𝜋ℎ(R+r)
• Total surface area=2𝜋(𝑅 + 𝑟)(𝑅 +
ℎ − 𝑟)
• Volume = 𝜋ℎ(R²+r²)

7. CONE(RIGHT CIRCULAR CONE)
For a right circular cone of height ‘h’ slant
height ‘l’ and radius of base ‘r’
• Slant height = 𝑟2 + ℎ²
• Total surface area = 𝜋𝑟 𝑙 + 𝑟
• Curved surface area = 𝜋𝑟𝑙
• Volume =
1
3
𝜋𝑟²ℎ

8. CONE(FRUSTUM OF CONE)
• Slant height = ℎ2 + (𝑅 − 𝑟)²
• Total surface area = 𝜋𝑙 𝑅 + 𝑟 +
𝜋(𝑅 + 𝑟)
• Volume =
1
3
𝜋ℎ (R+Rr+r²)
• Lateral surface area = 𝜋𝑙 (𝑅 + 𝑟)

9. SPHERE
• For a sphere of radius ‘r’ we have.
• Surface area = 4𝜋𝑟²
• Volume =
4
3
𝜋𝑟³

10. HEMI SPHERE
• For a hemi sphere of radius ‘r’ we
have.
• Surface area = 2𝝅𝒓 𝟐
• Total surface area = 3 𝝅𝒓 𝟐
• Volume =
𝟐
𝟑
𝝅𝒓³

11. END

12. SPHERICAL SHELL
• If ‘R’ and ‘r’ are respectively the outer
and inner radius of a spherical shell.
• Outer surface area = = 4𝜋𝑅2
• Volume = ==
4
3
𝜋(𝑅³ − 𝑟3)