A cube has each edge of length a. It is cut by a plane parallel to one face, dividing it into two parts with volumes in the ratio 1:3. What is the height of the smaller piece?

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EEJ MAIN Aptitude QUESTION #10964

Question 1

A cube has each edge of length \(a\. It is cut by a plane parallel to one face, dividing it into two parts with volumes in the ratio 1:3. What is the height of the smaller piece?

\(\dfrac{a}{3}\
\(\dfrac{a}{4}\✔️
\(\dfrac{a}{2}\
\(\dfrac{a}{6}\

Correct Answer Explanation

Let height of the cut from the bottom = \(h\.

Volume of smaller piece = \(a^2 \cdot h\

Total volume = \(a^3\

Ratio of smaller to larger: \(\dfrac{a^2 h}{a^3 - a^2 h} = \dfrac{1}{3}\

\(3a^2 h = a^3 - a^2 h\

\(4a^2 h = a^3\

\(h = \dfrac{a}{4}\

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