Question

A cube whose volume is 1/8 cubic centimetre is placed on top of a cube whose volume is 1 cm³ . The two cubes are then placed on top of a third cube whose volume is 8 cm³ . The height of the stacked cubes is
A. 3.5 cm
B. 3 cm
C. 7 cm
D. none of these

Answer 1

Given : A cube whose volume is 1/8 cm³ is placed on top of a cube whose volume is 1 cm³. The two cubes are then placed on top of a third cube whose volume is 8 cm³.  

 

Volume of 1st cube , V1 = 1/8 cm³

Volume of second cube , V2 = 1 cm³

Volume of third cube , V3 = 8 cm³

By using the formula of volume of cube  = a³ we find the edge of the cube :  

edge of the cube , a = ³√V

∴edge of first cube ,a1 = ³√1/8

a1 = ½ cm

∴ edge of second cube , a2 = ³√1

a2 = 1 cm

∴ edge of third cube , a3 = ³√8

a3 = 2 cm

Height of the stacked of cubes, H = a1 + a2 + a3

H = ½ + 1 + 2  

H = ½ + 3

H = (1 + 6)/2

H = 7/2  

H = 3.5 cm

Hence, the height of the stacked of cubes is 3.5 cm

Option (A) 3.5 cm is correct.

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Answer 2

Side of first cube = $\tt{\sqrt[3]{Volume}}$

Side = $\tt{\sqrt[3]{\frac{1}{8}}}$

Side = 1/2 = 0.5 cm

Side of second cube = $\tt{\sqrt[3]{Volume}}$

Side = $\tt{\sqrt[3]{1}}$

Side = 1 cm

Side of third cube = $\tt{\sqrt[3]{Volume}}$

Side = $\tt{\sqrt[3]{8}}$

Side = 2 cm

Height = sum of all the sides obtained = 0.5 + 1 + 2 = 3.5 cm

Answer is:- (A) 3.5 cm