To solve the problem, we first need to calculate the volume of Pyramid A and then compare it to the volume of Pyramid B to find how many times bigger Pyramid B's volume is than Pyramid A's volume.
Step 1: Calculate the volume of Pyramid A.
The formula for the volume \( V \) of a pyramid is: \[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Base Area of Pyramid A:
Since Pyramid A has a square base, we can calculate the base area as: \[ \text{Base Area} = \text{side length}^2 = 18^2 = 324 \text{ square inches} \]
Height of Pyramid A:
The height of Pyramid A is given as 9 inches.
Volume of Pyramid A:
Now we can substitute these values into the volume formula: \[ V_A = \frac{1}{3} \times 324 \times 9 \] Calculating this: \[ V_A = \frac{1}{3} \times 2916 = 972 \text{ cubic inches} \]
Step 2: Compare volumes of Pyramid A and Pyramid B.
The volume of Pyramid B is given as 3,136 cubic inches.
Step 3: Determine how many times bigger the volume of Pyramid B is than that of Pyramid A.
To compare the volumes, we can calculate the ratio: \[ \text{Ratio} = \frac{V_B}{V_A} = \frac{3136}{972} \]
Calculating this ratio: \[ \text{Ratio} \approx 3.225 (rounded to three decimal places) \]
Step 4: Convert the ratio to a percentage.
To find out how many times bigger Pyramid B is than Pyramid A in percentage, we take the ratio calculated, subtract 1 (the original volume of Pyramid A), and multiply by 100: \[ \text{Percentage Increase} = \left( \text{Ratio} - 1 \right) \times 100 \] Calculating this: \[ \text{Percentage Increase} = (3.225 - 1) \times 100 \approx 222.5 % \]
Conclusion
Pyramid B is approximately 222.5% bigger than Pyramid A's volume.
This indicates that Pyramid B's volume is more than three times the volume of Pyramid A, making it significantly larger in comparison.
5 answers