Which of these rectangular prisms has a base area of 40cm2 and a volume of 160cm3?
Answers are
C
D
C
D
C
thank you miku that’s all correct
yes miku is correct a
the answers are
C
D
C
D
C
these answers are correct 👍
Well, I must say, rectangular prisms with a base area of 40cm2 and a volume of 160cm3 are quite unique little creatures. It's like finding a unicorn in a field of cows. But fear not, my dear friend, for I have the answer to your oddly specific query. The rectangular prism that fits these whimsical specifications has a height of 4cm (since volume = base area × height) and a length and width of 10cm (since base area = length × width). Voila! The magical rectangular prism has been revealed.
To find the rectangular prism that has a base area of 40 cm² and a volume of 160 cm³, we need to consider the formula for the volume of a rectangular prism, which is given by:
Volume = Base Area * Height
Let's assume the dimensions of the rectangular prism are length (L), width (W), and height (H). We are given that the base area is 40 cm², so we have:
Base Area = Length * Width = 40 cm²
Next, we are given that the volume is 160 cm³, so we have:
Volume = Base Area * Height = 160 cm³
Now, let's solve the equations to find the dimensions of the rectangular prism. We can rearrange the first equation for the base area:
Length * Width = 40 cm²
Now, we substitute this value for the base area in the second equation:
40 cm² * Height = 160 cm³
Simplifying this equation:
Height = 160 cm³ / 40 cm² = 4 cm
Now that we know the height is 4 cm, we can substitute this value back into the first equation to solve for the length and width:
Length * Width = 40 cm²
Length * Width = 40 cm²
Since we have two variables and only one equation, there are multiple possibilities for the length and width that meet the given conditions. For example:
Length = 10 cm, Width = 4 cm
Length = 20 cm, Width = 2 cm
Length = 40 cm, Width = 1 cm
So, based on the given information, there are multiple rectangular prisms that can have a base area of 40 cm² and a volume of 160 cm³.