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
In a circular garden of radius 15 m, a path of 2 m wide has to be made inside the garden at the rate of ₹ 24 per sq. m. The cost of making the path is: (Take π = \(\frac{22}{7}\) )
A hollow cylinder with outer radius 4 cm and height 2 cm is made up of 1 cm thick metal sheet. What is the volume of metal used? (Take π = \(\frac{22}{7}\))
The length and breadth of a rectangular field are in the ratio 4 : 3. If the cost of cultivating the field at ₹2 per m 2is ₹600, then the length of the field is:
A cylindrical tank has a capacity of 5632 m3. If the diameter of its base is 8 m, what is the depth of the cylindrical tank? (Use π = \(\frac{22}{7}\))
Find the surface area of a sphere whose diameter is equal to 28 cm.
