What expression represents the height of this prism?
Volume = 64(c)3(b)8
Base area = 16(ab)3
a) 4a2b3
b) 4a3b3
c) 1024a3b9
d) 1024a4b9
To find the height of the prism, we need to use the formula for the volume of a prism. The formula is given as:
Volume = Base Area × Height
Given that the volume of the prism is 64(c)3(b)8 and the base area is 16(ab)3, we can substitute these values into the formula:
64(c)3(b)8 = 16(ab)3 × Height
Now, let's simplify the equation step by step:
First, let's simplify the components on both sides of the equation:
64(c)3(b)8 can be simplified as 4 × 4 × 4 × c × c × c × b × b × b × b × b × b × b × b
16(ab)3 can be simplified as 2 × 2 × a × a × a × b × b × b
Substituting these values into the equation, we get:
4 × 4 × 4 × c × c × c × b × b × b × b × b × b × b × b = 2 × 2 × a × a × a × b × b × b × Height
Now, let's cancel out the common factors on both sides of the equation:
4 × 4 × c × c × c × b × b × b × b × b × b = 2 × 2 × a × a × a × Height
We can simplify this further:
16c3b6 = 4a3 × Height
Next, let's isolate the height:
Divide both sides of the equation by 4a3:
16c3b6 / (4a3) = Height
Simplifying the right-hand side, we get:
4c3b6 / a3 = Height
So, the expression that represents the height of the prism is 4c3b6 / a3.
The correct answer is not provided in the options given.
I assume you meant:Volume = 4(c)^3(b)^8
Base area = 16(ab)^3
let the height be h
h(16(ab)^3) = 64(c)^3(b)^8
h = 4 c^3 b^5 /a^3
No choice is correct