Question

how does the total surface area of a box change if i) Each dimension is doubled ? ii)Each dimension is tripled? Express in words. Can you find the area if each dimension is raised to n times?

Answer 1

When each dimension of a box is doubled, the total surface area of the box is multiplied by a factor of 4. Similarly, when each dimension is tripled, the total surface area is multiplied by a factor of 9. If each dimension is raised to n times, the total surface area would be multiplied by a factor of n^2.

Step-by-step explanation:

When each dimension of a box is doubled, the total surface area of the box is multiplied by a factor of 4. For example, if the surface area of the original box is 10 square units, the surface area of the box with doubled dimensions would be 40 square units.

Similarly, when each dimension of a box is tripled, the total surface area of the box is multiplied by a factor of 9. Using the same example as before, if the surface area of the original box is 10 square units, the surface area of the box with tripled dimensions would be 90 square units.

If each dimension is raised to n times, the total surface area of the box would be multiplied by a factor of n^2. This means that for each dimension that is raised to n times, the surface area would be multiplied by a factor of n^2. For example, if one dimension is raised to 3 times and another dimension is raised to 2 times, the surface area would be multiplied by a factor of 3^2 and 2^2 respectively.