Question

26. The surface areas of the six faces of a rectangular solid are 16, 16,
32, 32, 72 and 72 square centimetres. The volume of the solid, in
cubic centimetres, is
(a) 192
(b) 384 (c) 480
(4) 2592​

Answer 1

Answer:

It's a very simple problem. But to understand the answer I am going to give you, you must give a great attention to it. Firstly, you have to imagine a cuboid, its dimensions and the structure.

Step-by-step explanation:

We know that area of any face of any cuboid is the product of its dimensions. I use the word DIMENSION for the length and breadth, because I don't know whether it is the length, breadth, or height of the face of that cuboid, which I am talking about.

So, your question was that, according to me, that if I let the dimensions be d(1), d(2), and d(3), then d(1)*d(2) = 16, d(2)*d(3) = 32, and d(3)*d(1) = 72, then what is the value of d(1)*d(2)*d(3) ?

So, since it is quite difficult to type for me, let the dimensions be x, y, and z.

So, we we talking that xy = 16, yz =32, and xz =72,

then I multiply the three values given.

Therefore, xy*yz*xz = 16*32*72,

Now I begine to solve according to the rules of Algebra, that x²*y²*z² =16*32*72,

now, I take square roots on the both sides of the equation, I get

√x²* y² * z² = √ 16*32*72,

then, x* y* z = 4*4*12,

= 196 cm²

So, I calculated the values of the product of the three dimensions, which is 196 cm².