Question

a solid right pyramid has a regular hexagonal base with an area of 7.4 units². the pyramid has a height of 6 units. what is the volume of the pyramid? 11.1 units³ 14.8 units³ 22.2 units³ 44.4 units³

Explanation:

Step1: Recall the volume formula for a pyramid

The volume \( V \) of a pyramid is given by the formula \( V=\frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height of the pyramid.

Step2: Identify the values of \( B \) and \( h \)

From the problem, the area of the base \( B = 7.4 \) units\(^2\) and the height \( h = 6 \) units.

Step3: Substitute the values into the formula

Substitute \( B = 7.4 \) and \( h = 6 \) into the formula \( V=\frac{1}{3}Bh \). So we have \( V=\frac{1}{3}\times7.4\times6 \).
First, calculate \( 7.4\times6 = 44.4 \), then divide by 3: \( \frac{44.4}{3}=14.8 \)? Wait, no, wait: \( \frac{1}{3}\times7.4\times6=\frac{7.4\times6}{3}=7.4\times2 = 14.8 \)? Wait, no, wait \( 7.4\times6 = 44.4 \), \( 44.4\div3 = 14.8 \)? Wait, no, wait the correct calculation: \( \frac{1}{3}\times7.4\times6=\frac{7.4\times6}{3}=7.4\times2 = 14.8 \)? Wait, no, wait 6 divided by 3 is 2, so 7.4 times 2 is 14.8? Wait, but let's check again. Wait, the base area is 7.4, height is 6. So \( V=\frac{1}{3}\times7.4\times6 \). Let's compute that: \( 7.4\times6 = 44.4 \), then \( 44.4\div3 = 14.8 \). Wait, but wait, maybe I made a mistake. Wait, no, the formula is \( V=\frac{1}{3}Bh \). So \( B = 7.4 \), \( h = 6 \). So \( V=\frac{1}{3}\times7.4\times6 = 7.4\times2 = 14.8 \)? Wait, no, 6 divided by 3 is 2, so 7.4*2=14.8. But wait, the options include 14.8? Wait, no, wait the options are 11.1, 14.8, 22.2, 44.4. Wait, but let's recalculate: \( \frac{1}{3}\times7.4\times6=\frac{7.4\times6}{3}=7.4\times2 = 14.8 \). So the volume is 14.8 units\(^3\). Wait, but wait, maybe I messed up the formula? No, the volume of a pyramid is one - third of the base area times height. So that's correct.

Wait, no, wait 7.4 times 6 is 44.4, divided by 3 is 14.8. Yes, that's correct.

Answer:

14.8 units\(^3\) (corresponding to the option: 14.8 units\(^3\))