Question

The volume of the
of the cone is 9856 cm3. . If the
diametre of the base is 28cm, find the
C.S.A of the cone.​

Answer 1

Answer:

$\bigstar{\bold{CSA\:of\:the\:cone=2200\:cm^{2}}}$

Step-by-step explanation:

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

• Volume of the cone = 9856 cm³
• Diameter of the base = 28 cm

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

• CSA of the cone

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

➟ Here we have to find the curved surface area of the cone

➟ First we have to find the height of the cone.

➟ Substituting it in the formula for volume, we get the value of height.

➟ Volume of a cone is given by,

   Volume of a cone = 1/3 × π r² h

➟ Substituting the data,

   9856 = 1/3 × 22/7 × 14 × 14 × h

   9856 = 1/3 × 22 × 2 × 14 × h

   h = 9856/205.33

   h = 48 cm

➟ Hence the height of the cone is 48 cm

➟ Now we have to find slant height (l) of the cone

➟ Slant height is given by,

    l = √(r² + h²)

➟ Substituting the data,

    l = √(14²) + (48²)

    l = √2500

    l = 50 cm

➟ Hence slant height of the cone is 50 cm

➟ Now we have to find the CSA

➟ CSA of a cone is given by,

    CSA of a cone = π r l

➟ Substitute the data,

    CSA of the cone = 22/7 × 14 × 50

    CSA of the cone = 2200 cm²

➟ Hence CSA of the cone is 2200 cm²

    $\boxed{\bold{CSA\:of\:the\:cone=2200\:cm^{2}}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

➟ The curved surface area of a cone is given by,

    CSA of a cone = π r l

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

    TSA of a cone = π r (r + l)

➟ Volume of a cone is given by,

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