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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]

Sagot :

GinnyAnswer
To find the volume of an oblique pyramid with a square base, we need to follow a series of steps. Let's go through them one by one.

1. Identify the given dimensions:
- Edge length of the square base ([tex]\( a \)[/tex]): 5 cm
- Height of the pyramid ([tex]\( h \)[/tex]): 7 cm

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

3. Calculate the volume of the pyramid:
- The volume ([tex]\( V \)[/tex]) of a pyramid is given by the formula [tex]\( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \)[/tex].
- Using the base area calculated and the given height:
[tex]\[ V = \frac{1}{3} \times 25 \times 7 \][/tex]
- Perform the multiplication:
[tex]\[ \frac{1}{3} \times 25 \times 7 = \frac{175}{3} \approx 58.333 \text{ cm}^3 \][/tex]

4. Convert the decimal result to a mixed number for the given choices:
- The value [tex]\( 58.333 \)[/tex] in mixed number form is [tex]\( 58 \frac{1}{3} \)[/tex].

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

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