A cone of radius 5 cm has curved surface area 1430/7 cm^2 find its volume.
Answers
Answer :
- The volume of the cuboid is 2200/7 cm³.
Explanation :
Given :
- Radius of the cone, r = 5 cm.
- Curved surface area of the cone, 1430/7 cm².
To find :
- Volume of the cone, v = ?
Knowledge required :
Formula for curved surface area of a cone :
⠀⠀⠀⠀⠀⠀⠀⠀⠀C.S.A. = πrl
Where,
- C.S.A. = Curved surface area of the cone.
- r = Radius of the cone.
- l = Slant height of the cone.
Formula for Slant height of a cone :
⠀⠀⠀⠀⠀⠀⠀⠀⠀l = √(h² + r²)
Where,
- l = Slant height of the cone.
- h = Height of the cone.
- r = Radius of the cone.
Formula for volume of a cone :
⠀⠀⠀⠀⠀⠀⠀⠀⠀v = ⅓πr²h
Where,
- v = Volume of the cone
- r = Radius of the cone
- h = Height of the cone
Solution :
To find the slant height of the cone :
By using the formula for Curved surface area of a cone and substituting the values in it, we get :
⠀⠀=> C.S.A. = πrl
⠀⠀=> 1430/7 = 22/7 × 5 × l
⠀⠀=> 1430/7 = 110l/7
⠀⠀=> 1430/7 × 7 = 110l
⠀⠀=> 1430 = 110l
⠀⠀=> 1430/110 = l
⠀⠀=> 13 = l
⠀⠀⠀⠀⠀⠀⠀∴ Slant height of the cone = 13 cm
Now let's find out the height of the cone :
⠀⠀=> l = √(h² + r²)
⠀⠀=> 13 = √(h² + 5²)
⠀⠀=> 13² = h² + 5²
⠀⠀=> 13² - 5² = h²
⠀⠀=> 169 - 25 = h²
⠀⠀=> 144 = h²
⠀⠀=> √144 = h
⠀⠀=> 12 = h
⠀⠀⠀⠀⠀⠀⠀∴ Slant height of the cone = 12 cm
To find out volume of the cone :
By using the formula for volume of a cone and substituting the values in it, we get :
⠀⠀=> v = ⅓πr²h
⠀⠀=> v = ⅓ × 22/7 × 5² × 12
⠀⠀=> v = ⅓ × 22/7 × 25 × 12
⠀⠀=> v = 22/7 × 25 × 4
⠀⠀=> v = 2200/7
⠀⠀⠀⠀⠀ ⠀⠀∴ v = 2200/7 cm³
Therefore,
- Volume of the cone, v = 2200/7 cm³