The edge of the cube is 6 cm. How much will the volume of the cube increase if each of its edges is reduced by 1 cm.
| April 11, 2021 | education
To determine the change in the volume of the indicated cube, we use the formula: ΔV = Vn – Vk = an ^ 3 – ak ^ 3 = an ^ 3 – (an – Δa) ^ 3, where an is the length of the edge of the original cube (an = 6 cm); Δа – change (decrease) in the length of the edge of the original cube (Δа = 1 cm).
Let’s make a calculation: ΔV = an ^ 3 – (an – Δa) ^ 3 = 6 ^ 3 – (6 – 1) ^ 3 = 216 – 5 ^ 3 = 216 – 125 = 91 cm3.
Answer: The volume of the indicated cube should decrease by 91 cm3 (increase by -91 cm3).
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