Question

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? $11\frac{2}{3}\\ \mathrm{cm}^3$ $43\frac{3}{4}\\ \mathrm{cm}^3$ $58\frac{1}{3}\\ \mathrm{cm}^3$ $87\frac{1}{2}\\ \mathrm{cm}^3$

Explanation:

Step1: Calculate base area

The base is a square, so area $A = s^2$ where $s=5$ cm.
$A = 5^2 = 25$ $\text{cm}^2$

Step2: Apply pyramid volume formula

Volume $V = \frac{1}{3} \times \text{base area} \times \text{height}$, height $h=7$ cm.
$V = \frac{1}{3} \times 25 \times 7 = \frac{175}{3}$

Step3: Convert to mixed number

$\frac{175}{3} = 58\frac{1}{3}$ $\text{cm}^3$

Answer:

$\boldsymbol{58\frac{1}{3}\ \text{cm}^3}$ (Option C)