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?
+23245 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
