Question

A solid cylinder of height 30cm and radius 10cm is melted and recast into cones if radius 3cm and height 2cm. Find the number of solid cones recast.​

Answer 1

Answer:

$\bigstar{\bold{Number\:of\:cones=500}}$

Step-by-step explanation:

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

• Height of the cylinder = 30 cm
• Radius of the cylinder = 10 cm
• Height of the cones = 2 cm
• Radius of the cones = 3 cm

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

• Number of solid cones recast

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

➣ Here we have to find the number of cones that can be recast from the solid cylinder.

➣ First we have to find the volume of the cylinder.

➣ Volume of a cylinder is given by,

   Volume of a cylinder = π r² h

    where r is the radius

    h is the height

➣ Substitute the data,

    Volume of the cylinder = 3.14 × 10² × 30

   Volume of the cylinder = 9420 m³

➣ Hence volume of the cylinder is 9420 m³.

➣ Now finding the volume of one of the cones.

➣ Volume of a cone is given by,

    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 × 3.14 × 3² × 2

    Volume of the cone = 18.84 m³

➣ Hence volume of each of the cone is 18.84 m³

➣ Now finding the number of cones that can be recast from it,

    Number of cones = Volume of cylinder/Volume of cone

➣ Substitute the data,

    Number of cones = 9420/18.84

    Number of cones = 500

➣ Hence 500 cones can be made from the solid cylinder.

    $\boxed{\bold{Number\:of\:cones=500}}$