. Doubling the dimensions makes the surface area 4 times the original surface area. Tripling the dimensions makes the surface area 9 times the original surface area.

Question 1083068: In order to triple the area of a square, the new side lengths must be equal to the old side lengths multiplied by: F) Square root of 3. J) Square root of 27. I selected “9”, but the answer is “F”, the square root of 3.

areas, of the figure or of the faces or surfaces of the object, change by the square of the same factor; So if you triple the length of all sides, the perimeter triples, the areas become 9 times as great, and if it’s a solid object, then the new, bigger one has 27 times the original volume.

18in. If you double all of the dimensions of a rectangular prism, you create a similar prism with a scale factor of 2. The surface area of the similar prism will increase as the square of the scale factor (22 = 4) and the volume will increase as the cube of the scale factor (23 = 8).

Lesson Summary When the dimensions of the shape, such as radius, height, or length change, both surface area and volume also change. However, the volume of the object always changes more than the surface area for the same change in dimensions.

When the dimensions are tripled, the volume is three times the original volume.

Justification: The volume of a cube of length x is x3. If the side length increases by a factor of F, the side length becomes Fx. The volume of the original cube was x3. When the side lengths were doubled, the surface area became (2x)3 = 8×3.

rectangular prism