a block prism has a volume of 36 cubic units, what is the least and greatest surface area it could have
To determine the least and greatest possible surface area of a block prism with a volume of 36 cubic units, we need to understand the relationship between volume and surface area.
A block prism typically has six faces: two identical bases and four identical lateral faces. Let's denote the length, width, and height of the block prism as L, W, and H respectively.
The volume of a block prism can be calculated using the formula: Volume = Length × Width × Height.
Given that Volume = 36 cubic units, we can find all the possible combinations of L, W, and H that satisfy this equation.
One way to approach this is by listing all the possible pairs of factors for 36. Factors are numbers that can be multiplied together to obtain a given product. In this case, the product is 36.
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Now, let's consider all possible combinations of the factors to find different length (L), width (W), and height (H) values that can satisfy Volume = L × W × H = 36.
For example, one possible combination is L = 1, W = 6, and H = 6, since 1 × 6 × 6 = 36. Another combination is L = 2, W = 3, and H = 6, since 2 × 3 × 6 = 36.
Once we have the different combinations, we can calculate the surface area of each block prism using the formula: Surface Area = 2(L × W + L × H + W × H).
By substituting the values of L, W, and H into this formula for each combination, we can find the corresponding surface area for each block prism.
After calculating the surface areas for all the combinations, we can determine the least and greatest possible surface area.
Simply compare the calculated surface areas to find the smallest and largest values among them.