Question

A solid sphere up of metal of radius 10.5cm is melted and recast into cones of smaller size each of radius 3.5cm and 3cm. How many such cones can be made from the sphere​

Answer 1

Answer:

cones can be made from the sphere is 126

Answer 2

Given:

Radius of metallic sphere=10.5 cm

Radius of cones of smaller size=3.5 cm

Height of cone= 3 cm

To Find:

Number of cones made from the sphere.

Solution:

Radius of sphere=$\dfrac{21}{2}$ cm

Volume of sphere:

$\dfrac{4}{3}\pi r^{2}=(\dfrac{4}{3}\pi \times \dfrac{21}{2}\times\dfrac {21}{2}\times\dfrac {21}{2})cm^{3}$

=$(\dfrac{3087\pi }{2}) cm^{3}$

Radius of each cone=$\dfrac{7}{2} cm$

Height of each cone=3 cm

Volume of each sphere:

$\dfrac{1}{3}\pi r^{2}h=(\dfrac{1}{3}\pi \times\dfrac{7}{2}\times\dfrac{7}{2}\times3)cm^{3}$

=$(\dfrac{49\pi}{4}) cm^{3}$

Number of cones:

$\dfrac{volume of the sphere}{volume of each cone}$

=$(\dfrac{3087\pi }{2}\times\dfrac{4}{49\pi})=126$

∴126 cones can be made from the sphere.