Two similar square prisms have base areas of 16ft^2 and 36 ft^2. The volume of the larger prism is 216 ft^3.

  a) What is the volume of the smaller prism?

  b) What is the height of the smaller prism?

  c) What is the lateral area of the larger prism?

 Apr 28, 2020

If two similar three-dimensional objects have corresponding areas of 16 ft2 and 36 ft2

their corresponding sides will be in the ratio as the square roots of these numbers:  4 ft and 6 ft

and their volumes will be in the ratio as the cubes of the sides:  64 ft3 and 216 ft3.


So, the smaller prism will have a volume of  (4 ft)3  =  64 ft3.


The height of the smaller prism is found by this formula:  V  =  (Area of Base) x (height)

                                                                                    64 ft3  =  16 ft2 x height     --->     height  =  4 ft


The lateral area of the larger prism, which is a square 6 ft on each side, is 6 x 36 ft2  =  216 ft2

 Apr 28, 2020

8 Online Users