Question

the volume of right circular cone is 9856cm³.If the radius of base 14 cm.find the----->
1. height of cone
2.Slant height
3. Total surface area of cone​

Answer 1

Given :-

The volume of the right circular cone

= 9856cm^3

Radius of the cone = 14cm

Solution 1 :-

Volume of the cone = 1/3πr^2h

Put the required values in the formula ,

9856 = 1/3 * 22/7 * 14 * 14 * h

h = 9856 * 3 * 7 / 22 * 14 * 14

h = 206976 / 4312

h = 48

Hence , The height of the cone is 48cm

Solution 2 :-

Radius of the cone = 14 cm

Height of the cone = 48cm

Now ,

( l )^2 = (radius)^2 + ( height )^2

Slant height ( l )^2 = √( 14)^2 + ( 48)^2

( l )^2 = 196 + 2304

( l )^2 = 2500

l = 50 cm

Thus , The slant height of a cone is 50 cm

Solution 3 :-

Total surface area of cone

$\pi r \: ( \:l \: + r \: )$

Put the required values in the formula ,

TSA of cone = 22/7 * 14 ( 50 + 14)

TSA of cone = 22 * 2 * 64

TSA of cone = 2816 cm^2

Answer 2

Answer :

• Height of the right-circular cone, h = 48 cm
• Slant height of the right-circular cone, l = 50 cm
• Total surface area of the cone, T.S.A. = 2816 cm²

Explanation :

Given :

• Volume of the right-circular cone, V = 9856 cm³
• Base radius of the cone, r = 14 cm

To find :

• Height of the right-circular cone, h = ?
• Slant height of the right-circular cone, l = ?
• Total surface area of the cone, T.S.A. = ?

Knowledge required :

• Formula for Volume of a right-circular cone :

⠀⠀⠀⠀⠀⠀⠀⠀⠀V = ⅓πr²h⠀

[Where : V = Volume of the right-circular cone; r = Base radius of the right-circular cone; h = Height of the right-circular cone]

• Formula for slant height of a right-circular cone :

⠀⠀⠀⠀⠀⠀⠀⠀⠀l = √(h² + r²)⠀

[Where : l = Slant height of the right-circular cone; r = Base radius of the right-circular cone; h = Height of the right-circular cone]

• Formula for Total surface of a right-circular cone :

⠀⠀⠀⠀⠀⠀⠀⠀⠀T.S.A. = πr(r + l)⠀

[Where : T.S.A. = Total surface area of the right-circular cone; r = Base radius of the right-circular cone; h = Height of the right-circular cone]

Solution :

To find the radius of the right-circular cone :

By using the formula for volume of a right-circular cone and substituting the values in it, we get :

⠀⠀=> V = ⅓πr²h

⠀⠀=> 9856 = ⅓ × 22/7 × 14² × h

⠀⠀=> 9856 × 3 = 22/7 × 196 × h

⠀⠀=> 9856 × 3 = 22 × 28 × h

⠀⠀=> 29568 = 616h

⠀⠀=> 29568/616 = h

⠀⠀=> 48 = h

⠀⠀⠀⠀⠀∴ h = 48 cm

Hence the height of the cone is 48 cm.

To find the slant height of the right-circular cone :

By using the formula for slant height of a cone and substituting the values in it, we get :

⠀⠀=> l = √(h² + r²)

⠀⠀=> l = √(48² + 14²)

⠀⠀=> l = √(2304 + 196)

⠀⠀=> l = √2500

⠀⠀=> l = 50

⠀⠀⠀⠀⠀∴ l = 50 cm

Hence the slant height of the cone is 50 cm.

To find the total surface area of the right-circular cone :

By using the formula for total surface area of a right-circular cone and substituting the values in it, we get :

⠀⠀=> T.S.A. = πr(r + l)

⠀⠀=> T.S.A. = 22/7 × 14 × (14 + 50)

⠀⠀=> T.S.A. = 22/7 × 14 × 64

⠀⠀=> T.S.A. = 22 × 2 × 64

⠀⠀=> T.S.A. = 2816

⠀⠀⠀⠀⠀∴ T.S.A. = 2816 cm²

Hence the total surface area of the cone is 2816 cm².