The difference in volumes of 2 cubes is 296 cm^3 and the difference in their one face areas is 28 cm^2. If the sum of their edges is 14 cm. then what is the product of their edges. Also what is the individual volumes and total surface areas of each cube
Solution(By Examveda Team)
Letter big cube has side A and small cube has side a.Sum of edges = 14 cm.
A +a = 14 ---------------- (1)
Difference of the volume of the cube = 296 cubic centimeter
Difference in one face area = 28 cm square.
Now,
A^2 - a^2 = 28
(A + a) (A -a) = 28
A - a = 2 ---------------- (2)
Adding equation (1) and (2)
A + A +a -a = 14 + 2
2A = 16
A = 8
So, a = 6.
Product of edges = A *a = 8 * 6 = 48
Volume of bigger cube = A3 = 8 *8 *8 = 512
Volume of smaller cube = 6 *6 *6 = 216
Surface are of bigger cube = 6A2 = 6 * 8 * 8 = 384.
Surface area for smaller one = 6 * 6 *6 = 216.
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