The areas of three adjacent faces of a rectangular box which meet in a point are known. The product of these areas is equal to _______.

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

The volume of the box.

Twice the volume of the box.

The square of the volume of the box.

The cube root of the volume of the box.

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

We know that a cuboid is a three dimensional object with six rectangular faces joined by 8 vertices. It has three different types of sides called length, breadth and height denoted l, b and h. The amount of space contained by a three dimensional object is measured by the quantity called volume. The amount of space that is occupied by a cuboid is the product of length, breadth and height. Mathematically, volume denoted as V a cuboid is

V = l × b × h = l b h

......(1)

https://www.vedantu.com/question-sets/269b214b-ea86-4cb5-8a3b-5244c8fdd9746966283203251421759.png

Let us denote the vertices of the cuboid as A, B, C, D, E, F, G, H. We are going to call two rectangular surfaces adjacent when they share a common vertex. We have the rectangular surfaces ABCD, DCFG and ADGH share the common vertex D. Let us assign
AB = HE = GF = CD = l
AD = BC = EF = GH = b
AH = GD = BE = CF = h
We are given the question that the areas of three adjacent faces of a rectangular box which meet in a point are known. The rectangular face is the product of its different sides. So the areas of three adjacent faces are