Question

The side of a solid cube is 12cm . Find lateral height of the square pyramid , that can be carved from the cube with maximum size ​

Answer 1

Given:

The side of the solid cube = 12 cm

To find:

The lateral height of the square pyramid, that can be carved from the cube with maximum size ​

Solution:

Since the a square pyramid with maximum size is to be carved from the cube

∴ Height of the pyramid = 12 cm ...... [the maximum height of the cube is 12 cm]

Also, the base of the square pyramid will have the same side length of 12 cm

Now, join the apex of the pyramid with a line segment at the midpoint of the base line.

By applying Pythagoras theorem, we get

Lateral/Slant height = $\sqrt{12^2\:+\:6^2} = \sqrt{144\:+\:36}= \sqrt{180} = 6\sqrt{5} \:cm\:or\:13.41 cm$

Thus, the lateral height of the square pyramid, that can be carved from the cube with maximum size ​is 6√5 cm or 13.41 cm.

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Also View:

The square pyramid of maximum size is carved out from a cube of side 12cm.

1.What is the length of the base edge?

2.what is height?

3.what is the volume?

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