Question

Four objects--A, B, C, and D--are all formed from 36 1 cm by 1 cm by 1 cm metal cubes. In all cases the cubes are stacked together with no gaps between them and all four objects use all 36 cubes. Answer the following questions about these objects and remember that explanations are required at all times.

2. If B is a rectangular prism--a box--with surface area of 72 cm squared, what are its dimensions, i.e., it length, width and height?

Answer 1

Let the length, breadth and height of Rectangular Prism be l cm, b cm and h cm respectively.

Volume of Rectangular Prism = l x b x h

Volume of 1 cube of given dimensions = 1 x 1 x 1

= 1 cm³

Number of cubes used = 36

Volume of Rectangular Prism/ Volume of cube = No. Of Cubes

Hence, ( l x b x h )/1 = 36

=> l x b x h = 36 cm³ - Eq.1

Surface Area = 72 cm²

2.(lb + bh + hl) = 72 cm²

lb + bh + hl = 36 cm² - Eq.2

On solving Eq.1 and Eq.2,

l = 6 cm, b = 3 cm, h = 2 cm

Which are the dimensions of Rectangular Prism.