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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
 #1
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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

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