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Answer:
PLease check your answer my dear friend
Step-by-step explanation:
To find out how many times bigger the volume of Pyramid B is compared to Pyramid A, we need to compare their volumes.
The volume \(V\) of a square pyramid can be calculated using the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
For Pyramid A, we can calculate its volume using the given dimensions:
\[ V_A = \frac{1}{3} \times (14 \text{ inches})^2 \times 6 \text{ inches} \]
\[ V_A = \frac{1}{3} \times 196 \text{ inches}^2 \times 6 \text{ inches} \]
\[ V_A = \frac{1}{3} \times 1176 \text{ cubic inches} \]
\[ V_A = 392 \text{ cubic inches} \]
Now, we'll compare this volume to the volume of Pyramid B, which is given as \(3136 \text{ cubic inches}\).
To find out how many times bigger Pyramid B is compared to Pyramid A, we divide the volume of Pyramid B by the volume of Pyramid A:
\[ \text{Times Bigger} = \frac{V_B}{V_A} = \frac{3136}{392} \approx 8 \]
So, Pyramid B is 8 times bigger in volume than Pyramid A.
To express this as a percentage increase:
\[ \text{Percentage Increase} = \left( \frac{\text{Volume of Pyramid B} - \text{Volume of Pyramid A}}{\text{Volume of Pyramid A}} \right) \times 100\% \]
\[ \text{Percentage Increase} = \left( \frac{3136 - 392}{392} \right) \times 100\% \]
\[ \text{Percentage Increase} = \left( \frac{2744}{392} \right) \times 100\% \]
\[ \text{Percentage Increase} \approx 700\% \]
So, the volume of Pyramid B is approximately 700% bigger than Pyramid A.
