Question

On the top face of the wooden cube of side 7 cm, hemispherical depressions of radius 0.35 cm are to be formed by taking out the wood. The maximum number of depressions that can be formed is ______.

Options

• 400

• 100

• 20

• 10

Answer 1

On the top face of the wooden cube of side 7 cm, hemispherical depressions of radius 0.35 cm are to be formed by taking out the wood. The maximum number of depressions that can be formed is 100.

Explanation:

Side of cube = 7 cm

Radius of hemispherical depression (r) = 0.35 cm

So, diameter = 2r

= 2 × 0.35

= 0.7 cm

On the top face (a square of side 7 cm), the maximum number of such depressions will be formed by placing them in rows and columns such that each depression occupies 0.7 cm along the side.

Number of depressions in one row = `7/07` = 10

Number of rows = `7/0.7` = 10

Therefore, maximum number of depressions on the top face = 10 × 10 = 100

Hence, the maximum number of depressions that can be formed is 100.