Given:
Volume of sphere = 1200 cm³
The sphere is dilated by a factor of [tex]\dfrac{3}{5}[/tex].
To find:
The volume of the dilated image.
Solution:
If two figures are similar then their volumes are proportional to cube of their corresponding sides.
We know that all sphere are similar to each other.
The sphere is dilated by a factor of [tex]\dfrac{3}{5}[/tex]. It means the ratio of new figure to original figure is
Let [tex]V_1[/tex] be the volume of original figure and [tex]V_2[/tex] be the volume of dilated figure.
[tex]\dfrac{V_2}{V_1}=\left(k\right)^3[/tex]
Where, k is the scale factor.
[tex]\dfrac{V_2}{1200}=\left(\dfrac{3}{5}\right)^3[/tex]
[tex]\dfrac{V_2}{1200}=\dfrac{27}{125}[/tex]
Multiply both sides by 1200.
[tex]V_2=\dfrac{27}{125}\times 1200[/tex]
[tex]V_2=259.2[/tex]
[tex]V_2\approx 259[/tex]
Therefore, the volume of the dilated image is 259 cubic centimetres.
