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?

Guest Apr 28, 2020

#1**+1 **

If two similar three-dimensional objects have corresponding areas of 16 ft^{2} and 36 ft^{2},

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 ft^{3} and 216 ft^{3}.

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

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

64 ft^{3} = 16 ft^{2} 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 ft^{2} = 216 ft^{2}

geno3141 Apr 28, 2020