Turn Up the Volume

Maggie Barnett

   Using a scale of two to dilate a shape I think would make the volume of that shape eight times greater. Using the scale factor of two to dilate a shape I believe would make the surface area of a shape four times greater.

Volume) V=Bh          B=45=(9)(5)           V=(45)(3)          Volume=135 cubic inches

Surface Area) S=Ph+2B      (40)(3)+(2)(27)          Surface Area=174 inches

Dilated Prism with a Scale Factor of 2

Volume) V=Bh        B=180=(18)(10)        V=(180)(6)        Volume=1080 cubic inches      

Surface Area) S=Ph+2B        (56)(6)+(2)(180)          Surface Area=696 inches


  Volume is the amount of space inside a three-dimensional figure. It is determined with the formula base multiplied by height. Finding the base is like finding the area of the bottom face of an object. The area of the base is multiplied by the height of the three-dimensional object. In this example, the area of the base was forty five square inches. Multiplied by the height of three you get a volume of 135 cubic inches.

   Surface Area is area the of all the faces on a three-dimensional object combined. It is determined with the formula perimeter multiplied by height added to the base multiplied by two. The base is determined by multiplying the length and width of the base. The perimeter is found by adding all the lengths of the sides together. In this example, the base was 27 square inches multiplied by two is 54 square inches. The perimeter was determined by adding all the sides of the object together which came to a sum of 40 inches. Multiplied by the height you get a product of 120. When added together you get the sum of 174 inches which is the surface area.

   My starting conjecture was correct. Since the volume of a dilated prism with a scale factor of two was eight times greater than the original volume of the cube. You can find this by multiplying 2 by 2 by 2 to get a product of eight. The length, width, and height are all multiplied by 2. My estimate for surface area was also correct since the surface area of the dilated prism was four times greater that the original surface area.