Answered

Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Writing an Algebraic Expression for Volume

The base edge of an oblique square pyramid is represented as [tex]x \, \text{cm}[/tex]. If the height is 9 cm, what is the volume of the pyramid in terms of [tex]x[/tex]?

A. [tex]3 x^2 \, \text{cm}^3[/tex]
B. [tex]9 x^2 \, \text{cm}^3[/tex]
C. [tex]3 \times \, \text{cm}^3[/tex]
D. [tex]x \, \text{cm}^3[/tex]

Sagot :

GinnyAnswer
Sure! Let's go through the solution step-by-step to find the volume of an oblique square pyramid in terms of [tex]\( x \)[/tex].

### Step-by-Step Solution

1. Identify the Variables:
- The base edge of the square pyramid is given by [tex]\( x \)[/tex] cm.
- The height of the pyramid is given as 9 cm.

2. Recall the Formula for the Volume of a Square Pyramid:
The volume [tex]\( V \)[/tex] of a square pyramid can be calculated using the formula:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]

3. Calculate the Base Area:
Since the base is a square with side length [tex]\( x \)[/tex], the area of the base [tex]\( A \)[/tex] is:
[tex]\[ A = x^2 \][/tex]

4. Substitute the Base Area and Height into the Volume Formula:
[tex]\[ V = \frac{1}{3} \times x^2 \times 9 \][/tex]

5. Simplify the Expression:
[tex]\[ V = \frac{1}{3} \times 9 \times x^2 \][/tex]
[tex]\[ V = 3 \times x^2 \][/tex]

Therefore, the volume of the oblique square pyramid, in terms of [tex]\( x \)[/tex], is given by:
[tex]\[ 3x^2 \, \text{cm}^3 \][/tex]

So the correct answer is:

[tex]\[ 3x^2 \, \text{cm}^3 \][/tex]
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.