Question

A metallic sphere 1 dm in diameter is beaten into a circular sheet of uniform thickness equal to 1 mm. Find the radius of the sheet.

Answer 1

Answer:

Radius of circular sheet is 40.8 cm.

Step-by-step explanation:

SOLUTION :  

Given :  

Diameter of a metallic sphere = 1 dm = 1 × 10 = 10 cm

[1 dm = 10 cm]

Thickness of circular sheet ,h = 1 mm = 1/10 cm  

[1 mm = 1/10 cm]

Radius of metallic sphere, R = 10/2 = 5 cm

Volume of metallic sphere,V1 = 4/3 πR³

V1 = 4/3 × π × 5³ = 4/3 × π × 125 = 500π/3 cm³

Let ,r be the radius of the circular sheet

Volume of circular sheet = Volume of metallic sphere

πr²h = 500π/3

r²(1/10) = 500/3

r² =  (500 × 10)/3  

r² = 5000/3  

r = √5000/3 = √1666.67

r = 40.8 cm

Hence, the Radius of circular sheet is 40.8 cm.

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Answer 2

Answer:

Step-by-step explanation:

Given:

Diameter of the metallic sphere = 1 dm = 10 cm.

Thickness of uniform circular sheet = 1mm.

To find: the radius of the sheet.

We know that diameter is twice the radius.

Thus, radius can be calculated by taking half of the diameter.

Hence, Radius of metallic sphere . $r=\frac{10}{2} cm$

It is given that, the thickness of the circular sheet is

h=1mm=$\frac{1}{10} cm$

Hence, by converting, the thickness of sheet is 0.1 cm.

We assume, r1 is the radius of sheet.

Now, colume of circular sheet will be the same as volume of metallic sphere.

Hence, we can write that,

Volume of circular sheet = volume of metallic sphere

$r_{1} ^2.h=\frac{4}{3}r^3\\ r_{1}^2.\frac{1}{10}=\frac{4}{3}.5^3\\r_{1} ^2=\frac{4.125.10}{3}=\frac{5000}{3}=r_{1} = \sqrt{\frac{5000}{3} } =40.8cm$

Therefore, the radius of the beaten circular sheet = 40.8 cm