Question

- If the radius of solid sphere is halved, then
the ratio of volume of original solid to the
resulting solid sphere is
(a) 5:2
(b) 8:1
(c) 2:5
(d) 1:8​

Answer 1

Answer:

b 8:1

Step-by-step explanation:

v1÷v2

4/3πr3 / 4/3π( r/2)3

r3/r3/8

8/1 means 8:1

Answer 2

Ratio of volume will be 1:8

So option (d) will be correct answer

Step-by-step explanation:

Let the radius of the circle is r

So volume of the sphere $V=\frac{4}{3}\pi r^3$

Now in second case radius is halved so new radius $r_{new}=\frac{r}{2}$

So new volume will be $V_{new}=\frac{4}{3}\pi r_{new}^3$, here $r_{new}=\frac{r}{2}$

So new volume will be equal to $V_{new}=\frac{4}{3}\pi (\frac{r}{2})^3=\frac{1}{6}\pi r^3$

Now we have to find the ratio of new volume and old volume

So $\frac{V_{new}}{V_{old}}=\frac{\frac{1}{6}\pi r^3}{\frac{4}{3}\pi r^3}=\frac{1}{8}$

So ratio of volume will be 1:8

So option (d) will be correct answer

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