To determine how many times bigger the volume of Pyramid B is compared to Pyramid A, and to express this ratio as a percentage, we can follow these steps:
### Step 1: Calculate the base area of Pyramid A
The base of Pyramid A is a square with each side being 18 inches. The area of a square is given by:
[tex]\[ \text{Area} = \text{side}^2 \][/tex]
So, for Pyramid A:
[tex]\[ \text{Base Area}_A = 18 \text{ inches} \times 18 \text{ inches} = 324 \text{ square inches} \][/tex]
### Step 2: Calculate the volume of Pyramid A
The volume of a pyramid is given by the formula:
[tex]\[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
So, for Pyramid A:
[tex]\[ \text{Volume}_A = \frac{1}{3} \times 324 \text{ square inches} \times 9 \text{ inches} \][/tex]
[tex]\[ \text{Volume}_A = \frac{1}{3} \times 2916 \text{ cubic inches} = 972 \text{ cubic inches} \][/tex]
### Step 3: Volume of Pyramid B
We are given that the volume of Pyramid B is 3,136 cubic inches.
### Step 4: Calculate the ratio of the volumes
To find out how many times bigger the volume of Pyramid B is compared to Pyramid A, we divide the volume of Pyramid B by the volume of Pyramid A:
[tex]\[ \text{Volume Ratio} = \frac{\text{Volume}_B}{\text{Volume}_A} \][/tex]
[tex]\[ \text{Volume Ratio} = \frac{3136 \text{ cubic inches}}{972 \text{ cubic inches}} \approx 3.226 \][/tex]
### Step 5: Convert the ratio to a percentage
To express this ratio as a percentage, we multiply it by 100:
[tex]\[ \text{Percentage Bigger} = 3.226 \times 100 \approx 322.633\% \][/tex]
### Conclusion
The volume of Pyramid B is approximately 3.226 times bigger than the volume of Pyramid A. Expressed as a percentage, Pyramid B is approximately 322.633% bigger than Pyramid A.
This indicates that Pyramid B's volume is more than three times larger than the volume of Pyramid A.
