K is a rectangular solid. Find the volume of K

easy one E.

Coz using both we can't get individual value of the sides or the product of the three sides.

MAGOOSH OFFICIAL SOLUTION:

So, the prompt gives us relatively little information. We are looking for the volume. Statement #1 tells us a diagonal line across the front face has a length of 40. If L is the length and H is the height, then this means: L^2 + H^2 = 40^2 = 1600. That’s one equation with two unknowns, and no way to solve for the volume.

Statement #1 by itself is insufficient.

Statement #2 tells us a diagonal line across the bottom face has a length of 25. If L is the length and W is the width, then this means: L^2 + W^2 = 25^2 = 625. Again, that’s one equation with two unknowns, and no way to solve for the volume. Statement #2 by itself is insufficient.

Combine the statements: we now know both L^2 + H^2 = 40^2 = 1600 and L^2 + W^2 = 25^2 = 625. We now have two equations but three unknowns: still not enough information to solve for the individual values, nor can we somehow rearrange to get the product of LWH. Even combined, the statements are insufficient.

Answer = E.

Check other 3-D Geometry Questions in our Special Questions Directory.

Rectangular solid refers to a Cuboid.

FROM STATEMENT - I ( INSUFFICIENT )

We can not find the volume of the Cuboid from the dimension of one diagonal.

FROM STATEMENT - II ( INSUFFICIENT )

Same as statement I , We can not find the volume of the Cuboid from the dimension of one diagonal.

\(FROM STATEMENT I AND II ( INSUFFICIENT )\)

We can not find the volume of a cuboid from the dimension of 2 diagonals , because the Volume of a Cuboid given the 3 diagonals as a , b and c is -

\(Volume \ of \ Cuboid = \sqrt{a^2 + b^2 + c^2}\)

Thus Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed , answer will be (E)

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