# two solid spheres made of the same metal have weights 5920 g and 740 g, respectively. determine the radius of the larger sphere, if the diameter of the smaller one is 5 cm.

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Two solid spheres made of the same metal have weights 5920 g and 740 g, respectively. Determine the radius of the sphere, if the diameter of the smaller one is 5 cm.

Video Solution Open in App Solution

Given, weight of one solid sphere,

m 1 = 5920 g

Weight of another solid sphere,

m 2 = 740 g

Diameter of the smaller sphere = 5 cm

∴

Radius of the smaller sphere,

r 2 = 5 2 , m 2 = 740 g We know that, D e n s i t y = M a s s ( M ) V o l u m e ( D ) ⇒ V o l u m e , V = M D ⇒ V 1 = 5920 D c m 3 … ( i ) V 2 = 740 D c m 3 … ( i i )

On dividing eq. (i) by eq. (ii), we get,

= V 1 V 2 = ( 5920 D ) ( D 740 )

[Density of the both spheres is same]

∵ Volume of a sphere = 4 3 π r 3 4 3 π r 3 1 4 3 π r 3 2 = 5920 740 ⇒ ( r 1 r 2 ) 3 = 592 74 ⇒ ( r 1 5 2 ) 3 = 592 74 [ ∵ r 2 = 5 2 c m ] ⇒ r 3 1 125 8 = 592 74 ⇒ 8 r 3 1 125 = 592 74 ⇒ r 3 1 = 592 74 × 125 8 = 74000 592 = 125 ∴ r 1 = 5 c m

Hence, the radius of the larger sphere is 5 cm.

Volume of a sphere

Standard IX Mathematics

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## Two solid spheres made of the same metal have weights 5920 g and 740 g, respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is 5 cm.

Click here👆to get an answer to your question ✍️ Two solid spheres made of the same metal have weights 5920 g and 740 g, respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is 5 cm.

Question

## Two solid spheres made of the same metal have weights 5920 g and 740 g, respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is 5 cm.

**A**

## 12 cm

**B**

## 2.5 cm

**C**

## 10 cm

**D**

## 5 cm

Medium Open in App

Updated on : 2022-09-05

Solution Verified by Toppr

Correct option is D)

Mass is directly proportional to volume for same metal (Density)

Let Mass of Solid 1 be M

1 , Volume be V 1

, Mass of Solid 2 be M

2 and Volume be V 2 Now M 2 M 1 = V 2 V 1

Volume of sphere is directly proportional to R

3 So, M 2 M 1 = V2 V1 = R 2 3 R 1 3 ⇒ 740 5920 = R 2 3 R 1 3 ⇒ R 2 3 R 1 3 =8 ⇒ R 2 R 1 = 3 8 ⇒ R 2 R 1 =2 So, R 1 =R 2 ×2 So, R 1 =2.5×2=5

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## Tow solid spheres made of the same metal have weight 5920 g and 740 g, respectively. Determine the radius of the radius of the larger sphere, if the diameter of the smaller one is 5 cm.

Let d g//cm^(3) be the density of the given metal and let the radius of the larger sphere be R cm Radius of smaller sphere = 2.5 cm. Now, ("volume of larger spher " xx d)/("volume of smaller sphere " xx d) = (5920)/(740) rArr ((4)/(3) pi R^(3) xxd)/((4)/(3) pi ((5)/(2))^(3) xxd)= 8 rArr R^(3) = 8 xx ((5)/(2))^(3) = (8 xx 125)/(8) = 125 rArr R^(3) = 5^(3) rArr R = 5 cm Hence, the radius of the larger sphere is 5 cm.

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Tow solid spheres made of the ...

Tow solid spheres made of the same metal have weight

5920g 5920g and 740g, 740g,

respectively. Determine the radius of the radius of the larger sphere, if the diameter of the smaller one is

5cm. 5cm.

Updated On: 27-06-2022

00 : 30

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Text Solution Open Answer in App Solution Let d g/c m 3 g/cm3

be the density of the given metal and let the radius of the larger sphere be

R R cm

Radius of smaller sphere

=2.5cm. =2.5cm. Now,

volume of larger spher ×d

volume of smaller sphere ×d

= 5920 740

volume of larger spher ×dvolume of smaller sphere ×d=5920740

⇒ 4 3 π R 3 ×d 4 3 π ( 5 2 ) 3 ×d =8⇒ R 3 =8× ( 5 2 ) 3 = 8×125 8 =125

⇒43πR3×d43π(52)3×d=8⇒R3=8×(52)3=8×1258=125

⇒ R 3 = 5 3 ⇒R=5cm ⇒R3=53⇒R=5cm

Hence, the radius of the larger sphere is

5cm. 5cm.

Answer

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Guys, does anyone know the answer?