Question

the ratio of the volumes of two spheres is 27: 64, If the sum of their radii are 28cm . What is the radius each of them.
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Answer 1

Given :-

• The ratio of the volumes of two spheres is

27:64.

• The sum of their radii are 28 cm.

To find :-

• The radii of two spheres.

Answer :-

Let the radius of the first sphere be r cm

Let the radius of the second sphere be

R cm

Volume of the first sphere = (4/3)πr³ cubic cm

Volume of the second sphere = (4/3)πR³ cubic cm

The ratio of their volumes

=> (4/3)πr³ : (4/3)πR³

=> (4/3)πr³ / (4/3)πR³

=> r³ : R³

According to the given problem

The ratio of their volumes = 27:64

Therefore, r³ : R³ = 27 : 64

=> r³/ R³ = 27 / 64

=> r³ / R³ = 3³ / 4³

=> (r/R)³ = (3/4)³

=> r / R = 3 / 4

=> r : R = 3 : 4

Let r = 3X cm

Let r = 3X cmLet R = 4X cm

Given that

The sum of their radii = 28 cm

=> r + R = 28

=> 3X + 4X = 28

=> 7X = 28

=> X = 28/7

=> X = 4 cm

If X = 4 cm then 3X = 3(4) = 12 cm

If X = 4 cm then 4X = 4(4) = 16 cm

Therefore, r = 12 cm and R = 16 cm

Answer :-

• The radii of the two spheres are

12 cm and 16 cm respectively.

Check :-

We have,

r = 12 cm

R = 16 cm

Their sum = 12+16 = 28 cm

Volume of the first sphere = (4/3)π(12)³ cm³

Volume of the second sphere = (4/3)π (16)³ cm³

Their ratio = (4/3)π(12)³ : (4/3)π (16)³

= (4/3)π(12)³ / (4/3)π (16)³

= 12³/16³

= (12/16)³

= (3/4)³

= 27/64

= 27:64

Verified the given relations in the given problem.

Used formulae:-

• Volume of the first sphere = (4/3)πr³ cubic units

• r = radius
• π = 22/7

Answer 2

GIVEN :-

• the ratio of the volumes of two spheres is 27: 64, If the sum of their radii are 28cm

TO FIND :-

• What is the radius each of them = ?

SOLUTION :-

radius of the small sphere be r and big sphere be R

volumes of two spheres are in the ratio = 27: 64

4/3 πr : 4/3 πr h = 27 :64

r1 and r2 = 27 :64

r1 and r2 = 3:4

then, we have

r1 = 3x , r2 = 4x

so ,we have

r1 + r2 = 28

3x + 4x = 28

7x = 28

x = 4

then, we have to multiply we get answer

= 3 × 4 = 12

= 4 × 4 = 16