karleee33
Answered

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A pyramid has a height of 10 inches and a base with an area of 21 square inches. Find the volume of the pyramid.

A. [tex]\( 210 \, in^3 \)[/tex]
B. [tex]\( 105 \, in^3 \)[/tex]
C. [tex]\( 70 \, in^3 \)[/tex]
D. [tex]\( 35 \, in^3 \)[/tex]

Sagot :

GinnyAnswer
To solve this problem, let's use the formula for the volume of a pyramid. The volume [tex]\( V \)[/tex] of a pyramid is given by:

[tex]\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \][/tex]

Let's break it down step by step:

1. Identify the height and the base area of the pyramid:
- Height ([tex]\( h \)[/tex]): 10 inches
- Base area ([tex]\( A \)[/tex]): 21 square inches

2. Substitute the given values into the formula for the volume of a pyramid:
[tex]\[ V = \frac{1}{3} \times 21 \times 10 \][/tex]

3. Calculate the volume:
[tex]\[ V = \frac{1}{3} \times 210 \][/tex]
[tex]\[ V = 70 \text{ cubic inches} \][/tex]

Thus, the volume of the pyramid is [tex]\( 70 \)[/tex] cubic inches.

So, the correct answer is:

C. [tex]\( 70 \ i^3 \)[/tex]

Answer: A

Step-by-step explanation: the volume of the pyramid is 210in

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