Question

A cone of radius 5 cm has curved surface area 1430/7 cm^2 find its volume.​

Answer 1

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