Question

the number of solid spheres,each of diameter 6cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm is​

Answer 1

Answer:

Number of spheres = 5

Step-by-step explanation:

Given:

• Height of the cylinder = 45 cm
• Diameter of the cylinder = 4 cm
• Diameter of the sphere = 6 cm

To Find:

• Number of spheres that can be made from the solid cylinder

Solution:

First finding the volume of the cylinder,

Volume of a cylinder is given by,

Volume of a cylinder = π r² h

where r is the radius

h is the height

Substitute the data,

Volume of the cylinder = π × (4/2)² × 45

Volume of the cylinder = 180 π cm³.

Now finding the volume of the sphere,

Volume of the sphere is given by,

Volume of the sphere = 4/3 × π × r³

where r is the radius

Substitute the data,

Volume of the sphere = 4/3 × π × (6/2)³

Volume of the sphere = 36 π cm³

Now finding the number of spheres that can be made,

Number of spheres = Volume of cylinder/Volume of sphere

Substitute the data,

Number of spheres = 180 π/36π

Number of spheres = 5

Hence 5 spheres can be made from the cylinder.

Answer 2

Answer:

Given :-

• Height of cylinder = 45 cm
• Diameter of cylinder = 4 cm
• Diameter of sphere = 6 cm

To Find :-

Total number of solids

Solution :-

As we know that

$\sf Volume \: of \: cylinder = \pi r {}^{2} h$

Firstly let's find Radius of cylinder

Radius = Diameter/2

Radius = 4/2

Radius = 2 cm

Now,

Let's find volume

$\sf \: Volume \: = \pi \: \times {2}^{2} \times 45$

$\sf \: Volume = \pi \: \times 4 \times 45$

$\sf \: Volume = {180\pi \: cm}^{3}$

Now,

Let's find Volume of sphere

$\sf Volume = \dfrac{4}{3} \times \pi \: \times {r}^{3}$

Let's find radius of sphere

Radius = Diameter/2

Radius = 6/2 = 3 cm

$\sf \: Volume = \dfrac{4}{3} \times \pi \times {9}^{3}$

$\sf \: Volume = 4 \times \pi \times 9$

$\sf \: Volume \: = 36\pi \: cm {}^{3}$

Now,

Let's find total sphere

$\boxed { \bf total \: sphere = \frac{ \bf volume \: of \: cylinder}{volume \: of \: sphere} }$

$\sf \: total \: sphere = \dfrac{180\pi}{36\pi}$

π will be cancelled

$\sf \: total \: sphere \: = \dfrac{180}{36} = 5$