Question
The volume of a cube is 21952 cm 3 in which
a maximum possible size of circle is drawn on each face. The circle drawn on each face of the cube is painted by pink colour at the rate of Rs. 12.5 per cm 2 and the remaining part of the cube is painted by the red colour at the rate of Rs. ‘y’ per cm 2 . If the total cost of painting the entire cube is Rs. 64848, then find out the value of ‘y’.Solution
The volume of a cube is 21952 cm3 . (Length of each side of cube)3 = 21952 Length of each side of cube = 28 cm A maximum possible size of circle is drawn on each face of the cube. Then the diameter of the circle is equal to the length of each side of the cube. diameter of the circle = 28 cm Radius of circle = 28/2 = 14 cm The circle drawn on each face of the cube is painted by pink colour at the rate of Rs. 12.5 per cm2 and the remaining part of the cube is painted by the red colour at the rate of Rs. ‘y’ per cm2. If the total cost of painting the entire cube is Rs. 64848. cost of painting each side of cube = 64848/6 = Rs. 10808 [12.5 x (22/7) x (radius)2] + [y x [28x28-[(22/7) x (radius)2]]] = 10808 Put the radius in the above equation. [12.5 x (22/7) x (14)2] + [y x [28 x 28-[(22/7) x (14)2]]] = 10808 [12.5 x (22/7) x 196] + [y x [784-[(22/7) x 196]]] = 10808 [12.5 x 616] + [y x [784-616]] = 10808 7700 + y x 168 = 10808 168y = 10808-7700 168y = 3108 Value of ‘y’ = 18.5
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