Question

A solid metallic sphere of diameter 21cm is melted and recast into a number of smaller cones,each of diameter 7cm and height 3cm.find the number of cones so formed.

Answer 1

Given:

diameter of bigger sphere= 21 cm

Diameter of smaller cones = 7cm

Height of smaller cones =3 cm

To Find:

Find the number of cones if the bigger sphere is melted to form the cones.

To Find:

Volume of the sphere = (πd³)/6.

                                     =(π×21³)/6

Volume of each cone = (πd²h)/12

                                    = (π×7²×3)/12

Let the numbers of cone = n

According to the question,

volume of the sphere = total volumes of the cone

(π×21³)/6 = n× (π×7²×3)/12

21³/6 = n×7²×3/12

n=7×3²×2

n=126

Hence the total numbers of cones are 126

Answer 2

Answer:

The number of cones so formed =126

Step-by-step explanation:

GIVEN:

  solid metallic sphere of diameter  $=21CM$

      solid metallic sphere of radius  $=\frac{21}{2} CM$

  And it is melted and recast into smaller cones.

   Smaller cone each diameter is $7CM$

  Smaller cone each radius is $=\frac{7}{2} =3.5$

   Smaller cone each height  is $3CM$

 Volume of the sphere is $=\frac{4}{3} *\pi *r^{3}$

                                            $=\frac{4}{3} *\pi *\frac{21}{2} ^{3} \\\\=4849.04 CM^{3}$

Volume of the cone is= $\frac{1}{3} *\pi *r^{2} *h$

                                      $=\frac{1}{3} *\pi *3.5^{2} *3\\=38.484x^{2} CM^{3}$

Let us consider n as number of cones formed

      n=$\frac{volume of sphere}{volume of cone}$

         $=\frac{4849.04}{38.48}$

       n  =126

The number of cones so formed IS 126

   

THE PROJECT CODE IS #SPJ2