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Chapter 12: Q38. (page 480)

A diagonal of a cube joins two vertices not in the same face. If the diagonals are43cm long, what is the volume?

Short Answer

Expert verified

The volume is 839cm3when the diagonals are43鈥塩尘 .

Step by step solution

01

Step 1. Given information.

A diagonal of a cube joins two vertices not in the same face and the diagonals are43cm long.

02

Step 2. Write the concept.

Since a diagonal of a cube joins two vertices not in the same face.

Then, the factor can be found as:

k=432=23cm

03

Step 3. Determine the volume.

Now, the ratio of the larger cube and smaller cube is cube of k factor,

vlvs=k3(43)2vs=(23)3[simplify]64vs=243[multiply]

Simplify the last expression,

vs=64243[crossmultiplication]=839[simplify]

Thus, the volume is 839鈥夆赌塩尘3when the diagonals are 43鈥夆赌塩尘.

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