**Student:** Dinkal Airen

**Q. How to solve volume and surface area questions. Can you explain the method. Here is the problem. A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes?**

**Answer : **

Hi Dinkal, Thanks for your Question.

**Summary :** To solve problems related to volume and surface area, we need to visualize the shapes, think through and solve as mentioned below.

**Concepts:**

- Cube is a solid with six congruent square faces.<
- A cube has six faces which are all squares, so each face has four equal sides and all four interior angles are right angles.
- A cube has 12 edges. Because all faces are squares and congruent to each other, all 12 edges are the same length.

**Method:** Say L is the length of any edge of a cube.

Then Volume of a Cube = *L * L * L = L ^{3}*

Surface Area of Cube : There are 6 faces of cube. Each face is square.

Surface area of one face = *L * L = L ^{2}*

Total Surface area of Cube =

*6 * L * L = 6L*

^{2}Now let`s solve the problem you mentioned.

The volume of the larger cube = *5 * 5 * 5 = 125 cm ^{3}. *

The volume of each of the smaller cubes =

*1 * 1 * 1 = 1 cm*

^{3}As volume would remain equal as same large cube is cut into smaller cubes.

Number of smaller cubes = *125/ 1 *

So there would be 125 smaller cubes.

The surface area of the larger cube = *6 * 5 * 5 = 150 cm ^{2}*

The surface area of each of the smaller cubes =

*6 * 1 * 1 = 6 cm*

^{2}Therefore, surface area of all of the 125 smaller cubes =

*125 * 6 = 750 cm*

^{2}.Surface area of larger cube =

*150 cm*

^{2}Surface area of all of the 125 smaller cubes =

*750 cm*

^{2}Therefore, the required ratio of surface area of larger cube to all smaller cubes = 150 : 750 = 1 : 5

Dinkal, Hope you got what you were looking for. Keep browsing the blogs for more examples. Post the query on home page if you have further questions.