Question

3) The volume of one sphere is 27 times that of another sphere. Calculate the ratio of their radii.
A) 1:27
B) 3:27
C) 9:81
D) 3:9​

Answer 1

Given:

• The volume of one sphere is 27 times that of another sphere.

To find:

• The ratio of their radii.

Solution:

❐ Let the volume of first sphere be r and volume of second sphere be R.

ATQ,

• volume of sphere = 27 × volume of second sphere

⇒ 4/3πr³ = 27 × 4/3πR³

⇒ r³ = 27R³

⇒ r³/R³ = 27/1

⇒ r/R = 3/1

Hence, the ratio of their radii is 3:1.

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Answer 2

Answer: 3:1

Step-by-step explanation:The volume of first sphere=27× volume of second sphere

Let the radius of the first sphere=r

1

​

And, radius of second sphere=r

2

​

Then, according to the question we have

3

4

​

πr

1

​

3

=27(

3

4

​

πr

2

​

3

)

r

2

​

3

r

1

​

3

​

=27

r

2

​

r

1

​

​

=

1

3

​

Thus, r

1

​

:r

2

​

=3:1