Aprism is enlarged by a factor of 4. the volume of the new prism is 576 cubic units. what could be the dimensions of the original prism?

a)3 by 3 by 1
b)2 by 3 by 6
c)6 by 3 by 8
d)4 by 4 by 4

Option (a) is correct.

3 by 3 by 1 could be the dimensions of the original prism.

Step-by-step explanation:

Given: A prism is enlarged by a factor of 4.   The volume of the new prism is 576 cubic units.

We have to choose the option from the given option that could be the dimensions of the original prism.

Volume of prism = Length × width  × height

Since, When A prism is enlarged by a factor of 4.

Then all its sides have been increased by a factor of 4.

The length of new prism = 4l

The width  of new prism = 4w

and the height of  of new prism = 4h

Then , Volume of new prism = 4L × 4w × 4h = 64 (l× w × h)

Given Volume of  new prism is 576 cubic units.

576 = 64 (l× w × h)

Divide both side by 64 , we have,

9 =  (l× w × h)

Thus, Out of given option only a) satisfies the product of three sides is 9

Thus, 3 by 3 by 1 could be the dimensions of the original prism.

Option (a) is correct.

3 by 3 by 1 could be the dimensions of the original prism.

Step-by-step explanation:

Given: A prism is enlarged by a factor of 4.   The volume of the new prism is 576 cubic units.

We have to choose the option from the given option that could be the dimensions of the original prism.

Volume of prism = Length × width  × height

Since, When A prism is enlarged by a factor of 4.

Then all its sides have been increased by a factor of 4.

The length of new prism = 4l

The width  of new prism = 4w

and the height of  of new prism = 4h

Then , Volume of new prism = 4L × 4w × 4h = 64 (l× w × h)

Given Volume of  new prism is 576 cubic units.

576 = 64 (l× w × h)

Divide both side by 64 , we have,

9 =  (l× w × h)

Thus, Out of given option only a) satisfies the product of three sides is 9

Thus, 3 by 3 by 1 could be the dimensions of the original prism.

found it xd it ok yt