Question

A solid right pyramid has a regular hexagonal base with an area of 5.2 cm2 and a height of h cm. Which expression represents the volume of the pyramid?

Answer 1

Welcome to QuestionCove (QC)! Before we start: Is there any extra information (drawings, diagrams, etc.) that would help us to focus on resolving this question?

Answer 2

Ok, so we have the following data:\[A=5.2\text{ cm}^2\]\[h=\text{? cm}\]Do you know the basic formula for pyramid volume?

Answer 3

not by hard

Answer 4

Which expression represents the volume of the pyramid?

Group of answer choices

1/3(5.2)h cm^3

1/3h (5.2)h cm^3

1/5 (5.2)h cm^3

1/5h (5.2)h cm^3

Answer 5

... wait. I think I left out a part in the formula 💀

Answer 6

maybe the fraction part?

Answer 7

Yeah... I have to double check to make sure the fraction part is right before I edit that up there

Answer 8

Why is the internet confusing me

Answer 9

maybe you need fresh air lol

Answer 10

i understand

Answer 11

Okay, okay

I was confused because the formula had a square root in it. But that's ONLY if you haven't calculated the area of the base, which you're already given. So the formula with area is actually\[\large{V=\frac{1}{3}b\cdot h}\]

Editing my explanation now.

Answer 12

Edited explanation, previous has been deleted

The formula for any pyramid's volume is: \(V=\frac{1}{3}b\cdot h\) where the variable \(b\) is the area of the base.

Here, you're given the base area already* as 5.2 square centimeters. So \(b=5.2\text{ cm}^{2}\). And your height is given as variable \(h\).
Thus, your formula can be written as\[V=\frac{1}{3}\color{crimson}{b}\cdot\color{olive}{h}=\frac{1}{3}\color{crimson}{5.2\text{ cm}^2}\cdot\color{olive}{h\text{ cm}}\]

* Sorry I made a typo earlier in my previous comment. It's not "A = 5.2 cm\(^{2}\)" but rather "b = 5.2 cm\(^2\)"
===
Now we simplify the formula:\[V=\frac{1}{3}5.2\text{ cm}^2\cdot h\text{ cm}\]\[V=\frac{1}{3}(5.2\cdot h)(\text{cm}^2\cdot\text{cm})\]Since we have a variable, we can take out the multiplication sign in the first part:\[V=\frac{1}{3}5.2h(\text{cm}^2\cdot\text{cm})\]Now we simplify the units part. Since \(\text{cm}^2=\text{cm}\cdot\text{cm}\), we will translate the expression into the following:\[V=\frac{1}{3}5.2h(\text{cm}\cdot\text{cm}\cdot\text{cm})\]Three of the same thing multiplied together is a "cube" with exponent 3.
As a result, your final expression should be:\[\Large{V=\frac{1}{3}5.2h\text{ cm}^3}\]

Answer 13

Ok, hopefully I didn't mess up this time. Does that make sense?

Answer 14

yes