Answered

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

GinnyAnswer
Certainly! Let's solve for the volume of an oblique pyramid that has a square base with an edge length of \(5 \text{ cm}\) and a height of \(7 \text{ cm}\).

### Step-by-Step Solution:

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

2. Use the formula for the volume of a pyramid:
The volume \(V\) of a pyramid is given by the formula:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
We already know the base area \(A = 25 \text{ cm}^2\) and the height \(h = 7 \text{ cm}\).
[tex]\[ V = \frac{1}{3} \times 25 \text{ cm}^2 \times 7 \text{ cm} \][/tex]
[tex]\[ V = \frac{1}{3} \times 175 \text{ cm}^3 \][/tex]
[tex]\[ V = 58.\overline{3} \text{ cm}^3 \][/tex]
This can also be written as:
[tex]\[ V = 58 \frac{1}{3} \text{ cm}^3 \][/tex]

3. Identify the correct answer from the given choices:
- \(11 \frac{2}{3} \text{ cm}^3\)
- \(43 \frac{3}{4} \text{ cm}^3\)
- \(58 \frac{1}{3} \text{ cm}^3\)
- \(87 \frac{1}{2} \text{ cm}^3\)

Based on our calculation, the volume of the pyramid is \(58 \frac{1}{3} \text{ cm}^3\), which matches one of the given options.

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