Select the correct answer.
Frances has 4 square baking dishes. Each pan is 7 inches$\times$7 inches$\times$2 inches. Which expression will give her the total volume of all the pans?
A. $7 \times 2 \times 2$
B. $7 \times 204$
C. $(7 \times 2 \times 2) \times 4$
D. $(7^2 \times 2) \times 4$
Answer (2)
The total volume of the four square baking dishes can be calculated by finding the volume of one dish as 7 × 7 × 2 = 98 cubic inches and then multiplying by 4, resulting in 392 cubic inches. The expression for this calculation is ( 7 2 × 2 ) × 4 . Therefore, the correct answer is option D.
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Calculate the volume of one baking dish by multiplying its length, width, and height: 7 × 7 × 2 = 98 cubic inches.
Multiply the volume of one baking dish by the number of dishes to find the total volume: 98 × 4 = 392 cubic inches.
Express the volume using exponents: ( 7 2 × 2 ) × 4 .
The expression that gives the total volume of all the pans is: ( 7 2 × 2 ) × 4
Explanation
Understanding the problem Let's break down this problem. Frances has several baking dishes, and we want to find the total volume they can hold. Each dish is a rectangular prism (since it has a length, width, and height), and we know how to find the volume of a rectangular prism. We also know how many dishes there are, so we can find the total volume.
Calculating the volume of one dish First, we need to find the volume of a single baking dish. The volume of a rectangular prism is found by multiplying its length, width, and height. In this case, the length is 7 inches, the width is 7 inches, and the height is 2 inches. So, the volume of one dish is:
7 inches × 7 inches × 2 inches = 98 cubic inches
Calculating the total volume Now that we know the volume of one dish, we need to find the total volume of all 4 dishes. To do this, we multiply the volume of one dish by the number of dishes:
98 cubic inches/dish × 4 dishes = 392 cubic inches
Matching the expression to the answer choices Now, let's look at the answer choices to see which expression matches our calculation. We calculated the total volume as ( 7 inches × 7 inches × 2 inches ) × 4 . This can also be written as ( 7 2 × 2 ) × 4 .
Comparing this to the answer choices, we see that option D, ( 7 2 × 2 ) × 4 , matches our expression.
Final Answer Therefore, the correct answer is D. ( 7 2 × 2 ) × 4 . This expression gives the total volume of all the pans.
Examples
Understanding volume is crucial in many real-world scenarios. For instance, when planning a garden, knowing the volume of soil needed for a raised bed helps ensure you purchase the correct amount, avoiding waste or shortages. Similarly, in cooking, understanding the volume of ingredients is essential for consistent and successful recipes. This concept extends to larger scales, such as calculating the capacity of storage tanks or the amount of water in a swimming pool, demonstrating its broad applicability.
