Question

Find the volume, the curved surface area and total surface area of a cone.
given that
(i) radius of base = 3.5 m and height = 12 m​

Answer 1

Answer:

Volume = 154 m³

CSA of the cone = 137.5 m²

TSA of the cone = 176 m²

Step-by-step explanation:

$\Large{\underline{\rm{Given:}}}$

• Radius = 3.5 m
• Height = 12 m

$\Large{\underline{\rm{To\:Find:}}}$

• Volume
• Curved surface area
• Total surface area

$\Large{\underline{\rm{Solution:}}}$

Volume of the cone:

↠ The volume of a cone is given by the equation,

    Volume of a cone = 1/3 × π × r² × h

    where r is the radius of the cone

     h is the height of the cone

↠ Substitute the data,

    Volume of the cone = 1/3 × 22/7 × 3.5 × 3.5 × 12

    Volume of the cone = 22 × 0.5 × 3.5 × 4

    Volume of the cone = 154 m³

↠ Hence volume of the cone is 154 m³.

Curved surface area:

↠ To find the CSA, we have to find the slant height of the cone.

↠ The slant height of a cone is given by,

    Slant height = √(r² + h²)

↠ Substituting the data,

    Slant height = √(3.5² + 12²)

    Slant height = √156.25

    Slant height = 12.5 m

↠ Now the CSA of a cone is given by,

   CSA of a cone = π r l

   where r is the radius and l is the slant height

↠ Substituting the values,

    CSA of the cone = 22/7 × 3.5 × 12.5

    CSA of the cone = 22 × 0.5 × 12.5

    CSA of the cone = 137.5 m²

↠ Hence curved surface area of the cone is 137.5 m².

Total surface area:

↠ The total surface area of a cone is given by,

    TSA of cone = π r (r + l)

↠ Substitute the data,

    TSA of the cone = 22/7 × 3.5 (3.5 + 12.5)

    TSA of the cone = 22 × 0.5 × 16

    TSA of the cone = 176 m²

↠ Hence the total surface area of the cone is 176 m².