The oblique pyramid has a square base with an edge length of [tex]5 \text{ cm}[/tex]. The height of the pyramid is [tex]7 \text{ cm}[/tex].

What is the volume of the pyramid?

A. [tex]11 \frac{2}{3} \text{ cm}^3[/tex]

B. [tex]43 \frac{3}{4} \text{ cm}^3[/tex]

C. [tex]58 \frac{1}{3} \text{ cm}^3[/tex]

D. [tex]87 \frac{1}{2} \text{ cm}^3[/tex]



Answer :

To find the volume of the pyramid, follow these steps:

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

2. Determine the shape and dimensions of the base:
In this case, the base of the pyramid is a square with an edge length of \( 5 \) cm.

3. Calculate the area of the square base:
The area \( A \) of a square is given by:
[tex]\[ A = \text{edge length}^2 \][/tex]
Substituting the given edge length:
[tex]\[ A = 5^2 = 25 \text{ cm}^2 \][/tex]

4. Use the height of the pyramid:
The given height \( h \) of the pyramid is \( 7 \) cm.

5. Apply the volume formula:
Substituting the base area \( A = 25 \text{ cm}^2 \) and the height \( h = 7 \text{ cm} \) into the volume formula:
[tex]\[ V = \frac{1}{3} \times 25 \text{ cm}^2 \times 7 \text{ cm} \][/tex]
Simplify the calculation:
[tex]\[ V = \frac{1}{3} \times 175 \text{ cm}^3 = 58.333\overline{3} \text{ cm}^3 \][/tex]

6. Match the calculation to the provided choices:
We convert the decimal \( 58.333\overline{3} \) to a fraction:
[tex]\[ 58.333\overline{3} = 58 \frac{1}{3} \][/tex]

Therefore, the volume of the pyramid is:

[tex]\[ 58 \frac{1}{3} \text{ cm}^3 \][/tex]

So, the correct answer is:
[tex]\[ 58 \frac{1}{3} \text{ cm}^3 \][/tex]