Question

12 solid spheres of the same size are made by melting a solid metallic cone of base radius 1cm and height 48cm.Find the radius of each sphere

Answer 1

Answer:

Radius of each sphere = 1 cm

Step-by-step explanation:

Given:

• Radius of the cone = 1 cm
• Height of the cone = 48 cm
• Number of spheres made = 12

To Find:

• The radius of each sphere

Solution:

First let us find the volume of the cone.

Volume of a cone is given by,

Volume of a cone = 1/3 × π × r² × h

Substitute the data,

Volume of the cone = 1/3 × 3.14 × 1² × 48

Volume of the cone = 50.24 cm³

Hence volume of the cone is 50.24 cm³.

Now by given the cone is melted to form all the 12 spheres.

Hence,

Volume of the cone = Volume of 12 spheres

Volume of the cone = 12 × Volume of a sphere

Volume of a sphere is given by,

Volume of a sphere = 4/3 × π × r³

Substitute the data,

12 × 4/3 × π × r³ = 50.24

352/7 × r³ = 50.24

r³ = 351.68/352

r³ =0.99 ≈ 1

r = ∛1

r = 1 cm

Hence radius of each of the sphere is 1 cm.

Answer 2

$\huge{\boxed{\rm{Question}}}$

12 solid spheres of the same size are made by melting a solid metallic cone of base radius 1 cm and height 48 cm .Find the radius of each sphere.

$\huge{\boxed{\rm{Answer}}}$

$\large{\boxed{\boxed{\sf{Given \: that}}}}$

• Number of spheres made = 12.

• Base radius of the cone = 1 cm.

• Height of the cone = 48 cm.

$\large{\boxed{\boxed{\sf{To \: find}}}}$

• Radius of each sphere.

$\large{\boxed{\boxed{\sf{Solution}}}}$

• Radius of each sphere = 1 cm.

$\large{\boxed{\boxed{\sf{What \: the \: question \: says}}}}$

$\large{\boxed{\boxed{\sf{Let's \: understand \: the \: concept \: 1st}}}}$

• This question says that there are 12 solid spheres of equal / same size. They are made by melting solid metallic cone of base radius 1 cm and it's height is 48 cm. Afterthat, it ask to find radius of each sphere.

$\large{\boxed{\boxed{\sf{How \: to \: solve \: this \: question}}}}$

$\large{\boxed{\boxed{\sf{Procedure \: of \: the \: question \: is \: given \: below}}}}$

• To solve this question firstly we have to know the rule to find volume of cone and we know what is the formula of it . Now, we have to put the Values according to this formula after that we get a result that is 50.24 cm³. And it's the volume of cone. Afterthat using the formula to find volume of sphere we have to putting the values after that we get 1 cm. And it's our final result . Hence, we get our answer.

$\large{\boxed{\boxed{\sf{Full \: solution}}}}$

According to the question let's carry on,

Firstly we have to find the volume of cone ! And we know that the what is the formula to find volume of cone. The formula is given below ✂

➙ Volume of cone = 1/3 × π × r² × h

Now, we have to putting the values according to this formula 1/3 × π × r² × h and we know that this formula is to find volume of cone !

Putting the values we get the following results ➳

☛ 1/3 × 3.14 × 1² × 48

☛ 50.24 cm³

Hence, 50.24 cm³ is the volume of cone.

According to the question let's carry on,

Now as we all know that a solid metallic cone is melted to form 12 spheres. Hence, we have to use the given formula ✂

➙ Volume of the cone = Volume of 12 spheres.

➙ Volume of the cone = 12 × volume of sphere

And we know what is the formula to find volume of sphere. The formula is given below ✂

➙ 4/3 × π × r³

Now, we have to putting the values according to this formula 4/3 × π × r³ and we know that this formula is to find volume of sphere !

Putting the values we get the following results ➳

☛ 12 × 4/3 × π × r³ = 50.24

☛ 12 × 4/3 × 22/7 × r³ = 50.24

☛ 352/7 × r² = 50.24

☛ 351.68/352

☛ r³ = 0.99

☛ r³ = 1

☛ r = ∛1

☛ r = 1 cm

Hence, 1 cm is the radius of each sphere.