Question

एक घनाभ के तीन संग्लन फलकों के क्षेत्रफल x, y और z है। यदि उसका आयतन v हो तो सिद्ध कीजिए कि v2= xyz​

Answer 1

Given data:

• A cube is given.
• The area of the adjacent faces are x, y and z.
• The volume of the cube is v.

To show: v² = xyz

Step-by-step explanation:

Let us take, length = a, width = b and height = c.

• Then the area of (a~b) surface is ab,
• the area of (b~c) surface is bc and
• the area of (c~a) surface is ca.

We consider: x = ab, y = bc and z = ca .....(1)

Now volume of the cube is

• v = a × b × c
• or, v² = (a × b × c)²
• or, v² = a × a × b × b × c × c
• or, v² = (a × b) × (b × c) × (c × a)
• or, v² = xyz, [by (1)]

Thus proved.