A rectangular prism has dimensions l > w > h. When viewed perpendicular to its largest face, the projected area is 60 sq.units. When viewed perpendicular to its medium face, the projected area is 40 sq.units. When viewed perpendicular to its smallest face, the projected area is 24 sq.units. What is the volume of the prism?

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EEJ MAIN Aptitude QUESTION #10992

Question 1

A rectangular prism has dimensions $l > w > h$. When viewed perpendicular to its largest face, the projected area is $60$ sq.units. When viewed perpendicular to its medium face, the projected area is $40$ sq.units. When viewed perpendicular to its smallest face, the projected area is $24$ sq.units. What is the volume of the prism?

$120$
$180$
$240$✔️
$360$

Correct Answer Explanation

Projected areas: $wh = 24$, $lh = 40$, $lw = 60$. Multiplying: $(lwh)^2 = 24 \times 40 \times 60 = 57600$. So $lwh = \sqrt{57600} = 240$. Volume = $240$ cubic units.

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