Question

A cube with a volume of 75 cm³ is dilated by a factor of 5. What is the volume of the dilated cube? Enter your answer in the box.

Answer 1

Volume of cube =75
`cm^(3)`

Volume of cube = length * width * height

A cube is dilated by factor 5 , which means the length, width and height each will be dilated by factor 5.

Volume of cube = (5* length) * (5*width) *(5* height)

Volume of cube = (5*5*5) *(length * width * height)

Volume of cube = 125 * 75

Volume of cube = 9375
`cm^(3)`

Answer 2

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. If the scale factor is greater than 1, the image is an enlargement.

If a figure is enlarged by a factor of five, the length will be five times greater, the width will be five times greater and the height will be five times greater.The volume will therefore be
`5^3` greater.

Hence

`V_(dilated)=5^3\cdot V_(initial), \\ v_(dilated)=5^3\cdot 75=125\cdot 75=9375 cm^3.`