A metallic cube of side 12 cm is cut into 8 equal solid cubes of equal volume. Find the ratio between the surface areas of a cube with a larger edge to a smaller edge.
4 : 1
The side of the original cube is 12 cm, and it is cut into 8 smaller cubes, so each smaller cube has a side of:
Side of smaller cube = 12 / 2 = 6 cm
Now, the surface area of a cube is given by the formula: Surface area = 6 × side2
Surface area of the larger cube (side = 12 cm):
Surface area = 6 × 122 = 6 × 144 = 864 cm2
Surface area of the smaller cube (side = 6 cm):
Surface area = 6 × 62 = 6 × 36 = 216 cm2
Thus, the ratio of the surface areas is:
Surface area ratio = 864 / 216 = 4 : 1
The ratio between the surface areas of a cube with a larger edge to a smaller edge is 4 : 1.
Important Questions from Mensuration
The areas of three adjacent faces of a cuboidal tank are 3 m 2, 12 m 2 and 16 m 2. the capacity of the tank, in litres, is:
Volume of a cuboid is 4800 cm 3. If the height of this cuboid is 20 cm, then what will be the area of the base of cuboid ?
Two similar cubes have heights of 8 cm and 12 cm, respectively. If the capacity of the smaller cube is 80 cm 3, what is the capacity of the bigger cube (in cm 3)?
Three circles of radius 7 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string?
Three circles of radius 6 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string?
