A cuboid is constructed with the dimensions as the longest diagonal of the cube, face diagonal of the cube of edge a cm, and the edge of the cube as length, breadth, and height, respectively. determine the ratio of the volumes of the cube and the cuboid.

Question

A cuboid is constructed with the dimensions as the longest diagonal of the cube, face diagonal of the cube of edge a cm, and the edge of the cube as length, breadth, and height, respectively. determine the ratio of the volumes of the cube and the cuboid. (A) 1: 9 (B) √6: 5 (C) 1: √6 (D) 3: √5

Tardigrade Admin · Accepted Answer

a3: √3 a × √2 a × a=1: √6

Q. A cuboid is constructed with the dimensions as the longest diagonal of the cube, face diagonal of the cube of edge a $c m$ , and the edge of the cube as length, breadth, and height, respectively. determine the ratio of the volumes of the cube and the cuboid.

$1 : 9$

$6 : 5$

$1 : 6$

$3 : 5$

$a^{3} : 3 a \times 2 a \times a = 1 : 6$

Q. A cuboid is constructed with the dimensions as the longest diagonal of the cube, face diagonal of the cube of edge a cm, and the edge of the cube as length, breadth, and height, respectively. determine the ratio of the volumes of the cube and the cuboid.

1:9

6​:5

1:6​

3:5​