# Turn up the volume

### Finding the volume and surface Area of a tissue box

How do you think the volume and surface area would be affected if you use a scale factor of 2 to dilate the shape?

I think that the shape would be affected greatly. The volume would have to be 6 times greater than the original, since each dimension is getting multiplied by 2. The surface area is a bit more confusing but, I think that the surface area would also multiply by 6. I think this since each dimension around the figure is also getting multiplied by 2.

# Dimensions

The dimensions of the tissue box are

Length-9 inches

Width-5 inches

height-3 inches

# Assignment

Volume of this figure is-  135 inches cubed. The equation is Bh, (base area x height) The base area is 45  (5 x 9) then multiply it by the height (45 x 3)

Surface area of this figure is- 174 inches squared. The equation is Ph + 2B. (perimeter of base x height + 2 x area of base) The perimeter of the base is 28 then multiply it by height to equal 84. Then the area of the base is 45, then multiply by 2. Add those together, to get to 174.

The net drawing of the tissue box

Dialation by 2.

The figures new volume is 1,080 inches cubed. You would have to multiply each dimension by 2, then multiply them together.

The new surface area is 588 inches squared. you need to find the new dimensions before you can use the appropriate equation.

# Reflection Essay

The way to calculate a prisms volume is a multi step equation. The equation of the volume of a prism is V= Bh. This stands for- volume= area of base x height of the prism. The first step is to find out your dimensions ( the length, width, and height). Once you find these, you multiply the length and width, to get the area of the base. Then you take that number and multiply it by the height to get your volume of a prism. In finding the volume of  prism, everybody must always work the problem backward to make sure the multiplication was correct.

The way to calculate a surface area of a prism, is totally different than the volume equation. The equation to find the surface area is Ph+2B. This means Perimeter of base x height + 2 multiplied by  the area of base. First you must find all the dimensions of the prism.  To start the equation, find the perimeter of the base and multiply it by the height. For the next part, multiply the area of the base by 2. That's how you find the surface area of a prism.Also make sure to check  your work for multiplication errors.

My conjecture was absolutely incorrect, the dilated volume is actually 8 times bigger than the original version. This calculation is correct because it would be 2 x 2 x 2 equaling up to a grand total of 8. My guess of the surface are was also a bit off. I was off because this ones only 4 x  bigger because you square this one not cube it. I did not factor in that this one is being squared.

The new figure is tremendously affected by the dilations. Since each dimension is 2 x bigger than the original it is affected greatly. The volume of the figure was 8 times bigger than the original and the surface are was 4 x bigger. Any figure is affected in a dilation since the dimensions are not the same. This matters because each figure has its own certain equation.