find the slant height, T.S.A,C.S.A and volume of right circular cone of 1) r =12m, h=5m. 2) r=1.4m, h=12cm . no spam .
Answers
Required Answer :
- The slant height of the cone = 13 m
- The total surface area of cone = 942.85 m²
- The curved surface area of cone = 490.28 m²
Given :
- Radius of the right circular cone = 12 m
- Height of the right circular cone = 5 m
To find :
- Slant height of the cone
- Total surface area of cone
- Curved surface area of cone
Solution :
Formula to calculate the slant height of the cone :
- Slant height of the cone = √(r² + h²)
where,
- r denotes the radius
- h denotes the height
Substituting the given values :
⇒ Slant height = √[(12)² + (5)²]
⇒ Slant height = √(144 + 25)
⇒ Slant height = √169
⇒ Slant height = ± 13 Reject - ve
⇒ Slant height = 13
Therefore, the slant height of the cone = 13 m
Formula to calculate the total surface area of the cone :
- Total surface area of the cone = πrl + πr²
where,
- Take π = 22/7
- r denotes the radius
- l denotes the slant height
Substituting the given values :
⇒ Total surface area = 22/7 × 12 × 13 + 22/7 × (12)²
⇒ Total surface area = 490.28 + 22/7 × 144
⇒ Total surface area = 490.28 + 452.57
⇒ Total surface area = 942.85
Therefore, the total surface area of cone = 942.85 m²
Formula to calculate curved surface area of cone :
- Curved surface area of cone = πrl
Substituting the given values :
⇒ Curved surface area = 22/7 × 12 × 13
⇒ Curved surface area = 490.28
Therefore, the curved surface area of cone = 490.28 m²
Required Answer :
- The slant height of the cone = 12.08 m
- The total surface area of cone = 59.312 m²
- The curved surface area of cone = 53.152 m²
Given :
- Radius of the right circular cone = 1.4 m
- Height of the right circular cone = 12 m
To find :
- Slant height of the cone
- Total surface area of cone
- Curved surface area of cone
Solution :
Formula to calculate the slant height of the cone :
- Slant height of the cone = √(r² + h²)
Substituting the given values :
⇒ Slant height = √[(1.4)² + (12)²
⇒ Slant height = √(1.96 + 144)
⇒ Slant height = √145.96
⇒ Slant height = ± 12.08 Reject - ve
⇒ Slant height = 12.08
Therefore, the slant height of the cone = 12.08 m
Formula to calculate the total surface area of the cone :
- Total surface area of the cone = πrl + πr²
Substituting the given values :
⇒ Total surface area = 22/7 × 1.4 × 12.08 + 22/7 × (1.4)²
⇒ Total surface area = 53.152 + 6.16
⇒ Total surface area = 59.312
Therefore, the total surface area of cone = 59.312 m²
Formula to calculate curved surface area of cone :
- Curved surface area of cone = πrl
Substituting the given values :
⇒ Curved surface area = 22/7 × 1.4 × 12.08
⇒ Curved surface area = 53.152
Therefore, the curved surface area of cone = 53.152 m²