Question

if a polyhedron has a volume of 35 cm^3 and is dilated by a factor of 5/2, what will be the volume of the dilated polyhedron? Round your answer to the nearest thousandth if necessary.

Answer 1

If a polyhedron has a volume of 35 cm cube and is dilated by a factor of 5/2 then the volume of dilated polyhedron will be 50.6 cm cube.

Given Volume of polyhedron=35 cm cube . Factor from which is dilated 5/2.

If the polyhedron is dilated by factor 5/2 then the volume of the polyhedron will change by the cube of that  factor because when it is dilated by factor its material also increases.

Volume =35$cm^{3}$

After dilation

Volume=35+$(5/2)^{3}$

=35+15.625

=50.625

After Rounding nearest to thousand we will get 50.6 $cm^{3}$.

Hence after dilation the volume which is 35 cm cube will change from 35 to 50.6$cm^{3}$.

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