The oblique pyramid has a square base with an edge length of 5 cm. The height of the pyramid is 7 cm.

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 an oblique pyramid with a square base and given dimensions, we can use the following steps:

1. Determine the area of the square base:
- The formula for the area [tex]\( A \)[/tex] of a square is given by:
[tex]\[ \text{Area} = \text{side length}^2 \][/tex]
- Here, the side length of the square base is 5 cm. So,
[tex]\[ \text{Area} = 5^2 = 25 \text{ cm}^2 \][/tex]

2. Calculate the volume of the pyramid:
- The formula for the volume [tex]\( V \)[/tex] of a pyramid is:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
- The base area we found is 25 cm[tex]\(^2\)[/tex], and the height of the pyramid is 7 cm. Plugging these values into the formula:
[tex]\[ V = \frac{1}{3} \times 25 \text{ cm}^2 \times 7 \text{ cm} \][/tex]

3. Perform the multiplication:
- First, multiply the base area by the height:
[tex]\[ 25 \text{ cm}^2 \times 7 \text{ cm} = 175 \text{ cm}^3 \][/tex]
- Next, take one-third of this product:
[tex]\[ V = \frac{1}{3} \times 175 \text{ cm}^3 = 58.33333333333333 \text{ cm}^3 \][/tex]

4. Express the volume:
- The volume in decimal form is approximately 58.33333333333333 cm[tex]\(^3\)[/tex].
- Converting this to a mixed number, we have approximately [tex]\( 58 \frac{1}{3} \)[/tex].

Therefore, the volume of the pyramid is [tex]\( 58 \frac{1}{3} \text{ cm}^3 \)[/tex].

The correct option is:
[tex]\[ \boxed{58 \frac{1}{3} \text{ cm}^3} \][/tex]