Question

Sphere A and Sphere B , are similar. The volumes of A and B, are 17 and 136 cubic centimetres, respectively. The diameter of B , is 6 centimetres. Determine the corresponding diameter of A. WRITE THE NUMERIC VALUE ONLY.

Answer 1

3

Explanation:

Given: Sphere A and Sphere B are similar.

The volumes of A and B are 17
`cm^3`and 136

The diameter of B is 6 cm.

To find: diameter of A

Solution:

Let R denotes radius of sphere A and r denotes radius of sphere B.

Radius of sphere A= R

Diameter of sphere B = 6 cm

So, radius of sphere B (r) =
`(6)/(2)=3\,\,cm`

Volume of sphere is
`(4)/(3)\pi(radius)^3`

Volume of sphere A =
`(4)/(3)\pi(R)^3`

`((4)/(3)\pi R^3)/((4)/(3)\pi r^3)=(17)/(136)=(1)/(8)\\(R^3)/(r^3)=(1)/(8)\\(R)/(r)=(1)/(2)\\r=2R`

Put r = 3 cm

`3=2R\\R=(3)/(2)=1.5\,\,cm`

Diameter of sphere A = 2 × Diameter

= 2 × 1.5

=3 cm