Previous Year Questions

Volume of the cube = Side * Side * Side

Side³ = 46656 cm³

Side = 36 cm

Four circles on each face on the cube means the diameter of each circle = 36/2 = 18 cm

Diameter of circle = 2 * Radius of the circle

The radius of the circle = Diameter of the circle/2

= 18/2

= 9 cm

The total number of circles drawn = 4 * the total number of faces of the cube

= 4 * 6

= 24

The total surface area of the cube = 6 * Side²

= 6 * 36²

= 7776 cm²

The area of a circle = π r²

The area of 24 circles = 24 * π * 9²

= 42768/7 cm²

The area of the remaining part of the cube = 7776 - 42768/7

= (54432 - 42768)/ 7

= 11664/7 cm²

The total cost of painting the remaining part of the cube = 11664/7 * 24.5

= Rs. 40824

Let the value that can fill the blank be 'a.

The cost of painting the 24 circles = The total cost of painting the entire cube - The total cost of painting the remaining part =

=> Rs. 104976 - Rs. 40824 = 42768/7 * a

=> Rs. 64152 = 42768/7 * a

=> a = 64152 * 7/ 42768

=> a = Rs. 10.5