Question

A cube whose volume is 1/8 cubic centimeter 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

Correct option is a 3.5 cm

Given,

Volume of 1^st cube = \(\cfrac{1}8cm^3\)

Volume of second cube = 1 cm³

Volume of third cube = 8 cm³

∴edge of first cube = a₁ =\(\sqrt[3]{\cfrac18}\) = \(\cfrac12\) cm

∴ edge of second cube = a₂ = \(\sqrt[3]1\) = 1 cm

∴ edge of third cube = a₃ = \(\sqrt[3]8\) = 2 cm

Hence height of cubes together = a₁ + a₂ + a₃ = \(\cfrac12\) + 1 + 2

= \(\cfrac72\) = 3.5 cm