Question

A solid metallic sphere of diameter 28cmis melted and re cast into a number of smaller cones , each diameter 4 2/3cm and height is 3cm.Find number of cones are formed​

Answer 1

ANSWER:

• The number of cones formed = 672

GIVEN:

• Diameter of the sphere = 28 cm

• It is melted and re-cast into a number of smaller cones.

• Diameter of cone = 4 2/3 cm

• Height of cone = 3 cm

TO FIND:

• The number of cones formed.

EXPLANATION:

• Let V be the volume of the sphere and v be the volume of the cone.

• Let R be the radius of the sphere and r br the radius of the cone.

• Let h be the height of the cone.

• Let n be the number of cones.

$\boxed{ \boxed{ \huge{ \bold{V = n \times v}}}}$

$\boxed{ \boxed{ \huge{ \bold{V = \dfrac{4}{3}\pi R^3}}}}$

$\boxed{ \boxed{ \huge{ \bold{v = \dfrac{1}{3}\pi r^2h}}}}$

$\dfrac{4}{3}\pi R^3 = n \times \dfrac{1}{3}\pi r^2h$

$4R^3 = n \times r^2h$

R = 28/2 = 14 cm

r = (4 2/3) ÷ 2 = (12 + 2) ÷ 6 = 14/6 = 7/3 cm

h = 3 cm

4 × 14 × 14 × 14 = n × 7/3 × 7/3 × 3

4 × 14 × 14 × 14 = n × 7/3 × 7

4 × 14 × 14 × 2 = n × 7/3

4 × 14 × 2 × 2 = n × 1/3

n = 14 × 16 × 3

n = 672

HENCE 672 CONES CAN BE MADE.

Answer 2

ANSWER

Solution:-

Solution:-Diameter of sphere = 28 cm

Solution:-Diameter of sphere = 28 cmThen, radius of sphere = 28/2 = 14 cm

Solution:-Diameter of sphere = 28 cmThen, radius of sphere = 28/2 = 14 cmvolume of the sphere = 4/3πr³

Solution:-Diameter of sphere = 28 cmThen, radius of sphere = 28/2 = 14 cmvolume of the sphere = 4/3πr³= 4/3*22/7*14*14*14

Solution:-Diameter of sphere = 28 cmThen, radius of sphere = 28/2 = 14 cmvolume of the sphere = 4/3πr³= 4/3*22/7*14*14*14Volume of sphere = 11498.66 cu cm

Solution:-Diameter of sphere = 28 cmThen, radius of sphere = 28/2 = 14 cmvolume of the sphere = 4/3πr³= 4/3*22/7*14*14*14Volume of sphere = 11498.66 cu cmDiameter of cone = 14/3 cm 

Solution:-Diameter of sphere = 28 cmThen, radius of sphere = 28/2 = 14 cmvolume of the sphere = 4/3πr³= 4/3*22/7*14*14*14Volume of sphere = 11498.66 cu cmDiameter of cone = 14/3 cm So, radius of cone = 14/3 ÷ 2

Solution:-Diameter of sphere = 28 cmThen, radius of sphere = 28/2 = 14 cmvolume of the sphere = 4/3πr³= 4/3*22/7*14*14*14Volume of sphere = 11498.66 cu cmDiameter of cone = 14/3 cm So, radius of cone = 14/3 ÷ 2radius of cone = 7/3

Solution:-Diameter of sphere = 28 cmThen, radius of sphere = 28/2 = 14 cmvolume of the sphere = 4/3πr³= 4/3*22/7*14*14*14Volume of sphere = 11498.66 cu cmDiameter of cone = 14/3 cm So, radius of cone = 14/3 ÷ 2radius of cone = 7/3Volume of the cone = 1/3πr²h

Solution:-Diameter of sphere = 28 cmThen, radius of sphere = 28/2 = 14 cmvolume of the sphere = 4/3πr³= 4/3*22/7*14*14*14Volume of sphere = 11498.66 cu cmDiameter of cone = 14/3 cm So, radius of cone = 14/3 ÷ 2radius of cone = 7/3Volume of the cone = 1/3πr²h= 1/3*22/7*7/3*7/3*3

Solution:-Diameter of sphere = 28 cmThen, radius of sphere = 28/2 = 14 cmvolume of the sphere = 4/3πr³= 4/3*22/7*14*14*14Volume of sphere = 11498.66 cu cmDiameter of cone = 14/3 cm So, radius of cone = 14/3 ÷ 2radius of cone = 7/3Volume of the cone = 1/3πr²h= 1/3*22/7*7/3*7/3*3Volume of cone = 17.11

Solution:-Diameter of sphere = 28 cmThen, radius of sphere = 28/2 = 14 cmvolume of the sphere = 4/3πr³= 4/3*22/7*14*14*14Volume of sphere = 11498.66 cu cmDiameter of cone = 14/3 cm So, radius of cone = 14/3 ÷ 2radius of cone = 7/3Volume of the cone = 1/3πr²h= 1/3*22/7*7/3*7/3*3Volume of cone = 17.11Number of cones formed = 11498.66/17.11

Solution:-Diameter of sphere = 28 cmThen, radius of sphere = 28/2 = 14 cmvolume of the sphere = 4/3πr³= 4/3*22/7*14*14*14Volume of sphere = 11498.66 cu cmDiameter of cone = 14/3 cm So, radius of cone = 14/3 ÷ 2radius of cone = 7/3Volume of the cone = 1/3πr²h= 1/3*22/7*7/3*7/3*3Volume of cone = 17.11Number of cones formed = 11498.66/17.11= 672 cones 

Solution:-Diameter of sphere = 28 cmThen, radius of sphere = 28/2 = 14 cmvolume of the sphere = 4/3πr³= 4/3*22/7*14*14*14Volume of sphere = 11498.66 cu cmDiameter of cone = 14/3 cm So, radius of cone = 14/3 ÷ 2radius of cone = 7/3Volume of the cone = 1/3πr²h= 1/3*22/7*7/3*7/3*3Volume of cone = 17.11Number of cones formed = 11498.66/17.11= 672 cones Answer.

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