Question

One day Rinku was going home from school, saw a carpenter working on wood. He found that he is carving out a cone of same height and same diameter from a cylinder. The height of the cylinder is 24 cm and base radius is 7 cm. While watching this, some questions came into Rinku minds. Help Rinku to find the answer of the following questions. i) Find the slant height of the conical cavity so formed. ii) The curved surface area of the conical cavity so formed. iii) External curved surface area of the cylinder iv) Volume of conical cavity.​

Answer 1

Answer:

I)l=√576+49

=√625

=25cm

ii)

CSA of cone = πrl

=22/7×7×25

=22*25

=550cm2

iii)

CSA of cylinder =2πrh

=2×22/7*7*24

=44*24

=1056cm2

iv)

volume of cone=1/3πr2h

=1/3*22/7*49*24

=22*7*8

=22*56

=1232cm3

Answer 2

Answer:

• The slant height of the conical cavity is 25 cm
• The curved surface area of the conical cavity so formed is

        549.8 cm²

• The external curved surface area of the cylinder is 1055.6 cm²
• The volume of the conical cavity is 1231.5 cm³

Step-by-step explanation:

Step 1 of 4: To find the Slant height of the cone

• Slant Height is given by

$l^{2} = h^{2}+r^{2}$

Where l is slant height, h is the height of the cone,r = radius of the cone

• Given :  $r=7 cm ,\ h=24 cm$

         $l^{2} = h^{2}+r^{2}\\l^{2} = 24^{2}+7^{2}\\l^{2} =576+49\\l^{2} = 625\\l=\sqrt{625} \\l=25 cm$

Step 2 of 4: To find the curved surface area of the conical cavity

• curved surface area is given by

     $CSA=\pi rl$

     $CSA=\pi *7*25\\CSA=549.8 cm^{2}$

Step 3 of 4: To find the curved surface area of the cylinder

• curved surface area is given by

      $CSA =2\pi rh\\CSA =2\pi *7*24\\\\CSA =1055.6 cm^{2}$

Step 4 of 4: To find the volume of the cone

• The volume of the cone is given by $\frac{1}{3} \pi r^{2} h$

       $V=\frac{1}{3}\ *\frac{22}{7} *7^{2}*24$

        $V=1232cm$³