Question

A cube whose edge is 21 cm long has a circle of diameter 21 cm on each of its faces painted black. What is the total area of the unpainted surface of the cube?

Answer 1

We have,

A cube whose edge is 21 cm long has a circle of diameter 21 cm each of its faces painted black.

Then, radius of a circle is `21/2` cm

Now we know that,

Total surface area of a cube is 6 edge² 

Then, total surface area of a cube is 621² = 2646 cm²

Now, area of a circle is πr² = `22/7 xx 21/2 xx 21/2` = 346.5 cm²

Then, the area of 6 circles is 6 × 346.5 = 2079 cm²

The total area of the unpainted surface of the cube = Total surface area of the cube – The area 6 circles

= 2646 – 2079

= 567 cm²

Therefore, the total area of the unpainted surface of the cube is 567 cm².