From a solid cube of side 24 cm, a cuboidal cavity of square cross-section of side 9 cm is hollowed along one

Question

From a solid cube of side 24 cm, a cuboidal cavity of square cross-section of side 9 cm is hollowed along one surface from one edge to the opposite edge. What is the volume (in cm 3 ) of the remaining solid?

Examoogle · Accepted Answer

The correct answer is Option A: 11880. Calculate volume of cube ($24^3 = 13824$) and subtract volume of the rectangular bar removed ($9 	imes 9 	imes 24 = 1944$). Since $13824 - 1944 = 11880$, the result is straightforward.

Step-by-Step Solution & Concepts:
Shortcut Trick: Calculate volume of cube ($24^3 = 13824$) and subtract volume of the rectangular bar removed ($9 	imes 9 	imes 24 = 1944$). Since $13824 - 1944 = 11880$, the result is straightforward.

Formula Used: $$V_{	ext{remaining}} = V_{	ext{cube}} - V_{	ext{cavity}} = (s^3) - (a^2 	imes l)$$

Given: Side of solid cube = 24 cm, side of square cross-section of cuboidal cavity = 9 cm, length of cavity = 24 cm (from one edge to opposite edge).

Steps: Calculate Volume of the solid cube: The volume of a cube is given by $V = s^3$, where $s$ is the side length.. Calculate Volume of the cuboidal cavity: The cavity is a cuboid with square cross-section $9 	ext{ cm} 	imes 9 	ext{ cm}$ and length equal to the cube side $24 	ext{ cm}$.. Calculate Remaining Volume: Subtract the cavity volume from the total cube volume to find the remaining material.

Answer: A is correct because the volume of the original cube is 13824 and subtracting the 1944 volume of the hollowed cuboid results in 11880.

Exam Tip: This concept of 'subtraction of volumes' is frequently used in engineering aptitude tests involving material removal processes like milling or drilling.

Examoogle · Answer

Option B: 13095

Examoogle · Answer

Option C: 8640

Examoogle · Answer

Option D: 12055 Question ID : 44100925521 Option 1 ID : 441009101789 Option 2 ID : 441009101787 Option 3 ID : 441009101790 Option 4 ID : 441009101788 Status : Answered Chosen Option : B

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