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

Answer:

3

Step-by-step 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) = $\frac{6}{2}=3\,\,cm$

Volume of sphere is $\frac{4}{3}\pi(radius)^3$

Volume of sphere A = $\frac{4}{3}\pi(R)^3$

$\frac{\frac{4}{3}\pi R^3}{\frac{4}{3}\pi r^3}=\frac{17}{136}=\frac{1}{8}\\\frac{R^3}{r^3}=\frac{1}{8}\\\frac{R}{r}=\frac{1}{2}\\r=2R$

Put r = 3 cm

$3=2R\\R=\frac{3}{2}=1.5\,\,cm$

Diameter of sphere A = 2 × Diameter

= 2 × 1.5

=3 cm