Question

A solid metallic sphere of radius 5.6 cm is melted and solid cones each of radius 2.8 cm and height 3.2 cm are made. Find the number of such cones formed.

Answer 1

Answer:

The number of cones formed is 28 .

Step-by-step explanation:

Given :  

Radius of solid metallic sphere , R = 5.6 cm  

Radius of solid cone , r = 2.8 cm  

Height of the solid cone , h = 3.2 cm

Number of cones = Volume of the solid metallic sphere / Volume of the Solid cone

= 4/3πR³ / 1/3πr²h

= 4R³ / r²h

= 4 × (5.6)³ / 2.8² × 3.2

= (4 × 5.6 × 5.6 × 5.6) / (2.8 × 2.8 × 3.2)

=  2 × 2 × 7

Number of cones = 28

Hence, Number of cones is 28 .

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Answer 2

$\underline{\textbf{Question}}$

A solid metallic sphere of radius 5.6 cm is melted and solid cones each of radius 2.8 cm and height 3.2 cm are made. Find the number of such cones formed.

$\underline{\textbf{Answer}}$

Radius of Sphere=5.6cm

$\mathbf{Volume\:\frac{4}{3}\pi\times{r}^{3}}$

$\mathbf{\frac{4}{3}\times\frac{22}{7}\times{5.6</p><p>}^{3}}$

$\mathbf{Volume\:of\:sphere=735.62 {m}^{3}}$

It is now melted And made into Cone.

Both Volume will same.

Radius=2.8 cm

Height=3.2 cm

$\mathbf{\pi {r}^{2} \frac{h}{3} }$

$\mathbf{ \frac{22}{7} \times 2.8 {}^{2} \times \frac{3.2}{3}}$

$\mathbf{Volume=26.08 {m}^{3}}$

$\boxed{\mathbf{Total\: Cone=\frac{Volume\:of\:sphere}{Volume\:of\:a\:Cone}}}$

$\boxed{\mathbf{Total\: Cone=\frac{735.62}{26.08}}}$

=28.2

Approx=28 cone

$\boxed{\mathbf{Total\:Cone=28}}$