Luis models the volume of a popcorn box as a right rectangular prism. Its dimensions are 3(1)/(2) in by 2 in by 6(3)/(4) in. How many cubic inches of popcorn would it hold when it is full? Round your answer to the nearest tenth if necessary.

Convert to Improper Fractions: To find the volume of a right rectangular prism, we use the formula Volume = length × width × height. The given dimensions of the popcorn box are 3(1/2) inches by 2 inches by 6(3/4) inches. We need to convert the mixed numbers to improper fractions to make the multiplication easier.Calculate Volume: First, convert 3(1/2) inches to an improper fraction. 3(1/2) inches is the same as (3 × 2 + 1)/2 inches, which equals 7/2 inches.Simplify Multiplication: Next, convert 6(3/4) inches to an improper fraction. 6(3/4) inches is the same as (6 × 4 + 3)/4 inches, which equals 27/4 inches.Divide to Find Volume: Now, multiply the dimensions together to find the volume. The volume V is given by V = length × width × height, so V = (7/2) inches × 2 inches × (27/4) inches.Round to Nearest Tenth: Simplify the multiplication. First, multiply the numerators together: 7 × 2 × 27. Then, multiply the denominators together: 2 × 1 × 4.The multiplication of the numerators gives us 7 × 2 × 27 = 14 × 27 = 378. The multiplication of the denominators gives us 2 × 1 × 4 = 8.Now, divide the result from the numerators by the result from the denominators to get the volume in cubic inches: 378/8 cubic inches.To simplify 378/8, we perform the division. 378 divided by 8 equals 47.25 cubic inches.The question asks for the volume rounded to the nearest tenth. 47.25 rounded to the nearest tenth is 47.3 cubic inches.

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Luis models the volume of a popcorn box as a right rectangular prism. Its dimensions are
3(1)/(2) in by 2 in by
6(3)/(4) in. How many cubic inches of popcorn would it hold when it is full? Round your answer to the nearest tenth if necessary.

Luis models the volume of a popcorn box as a right rectangular prism. Its dimensions are $3 \frac{1}{2}$ in by $2$ in by $6 \frac{3}{4}$ in. How many cubic inches of popcorn would it hold when it is full? Round your answer to the nearest tenth if necessary.

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Q. Luis models the volume of a popcorn box as a right rectangular prism. Its dimensions are

3 \frac{1}{2}

in by

2

in by

6 \frac{3}{4}

in. How many cubic inches of popcorn would it hold when it is full? Round your answer to the nearest tenth if necessary.

Convert to Improper Fractions: To find the volume of a right rectangular prism, we use the formula $\text{Volume} = \text{length} \times \text{width} \times \text{height}$ . The given dimensions of the popcorn box are $3\left(\frac{1}{2}\right)$ inches by $2$ inches by $6\left(\frac{3}{4}\right)$ inches. We need to convert the mixed numbers to improper fractions to make the multiplication easier.
Calculate Volume: First, convert $3(1/2)$ inches to an improper fraction. $3(1/2)$ inches is the same as $(3 \times 2 + 1)/2$ inches, which equals $7/2$ inches.
Simplify Multiplication: Next, convert $6\left(\frac{3}{4}\right)$ inches to an improper fraction. $6\left(\frac{3}{4}\right)$ inches is the same as $\left(6 \times 4 + 3\right)/4$ inches, which equals $\frac{27}{4}$ inches.
Divide to Find Volume: Now, multiply the dimensions together to find the volume. The volume $V$ is given by $V = \text{length} \times \text{width} \times \text{height}$ , so $V = (\frac{7}{2})$ inches $\times 2$ inches $\times (\frac{27}{4})$ inches.
Round to Nearest Tenth: Simplify the multiplication. First, multiply the numerators together: $7 \times 2 \times 27$ . Then, multiply the denominators together: $2 \times 1 \times 4$ .
Round to Nearest Tenth: Simplify the multiplication. First, multiply the numerators together: $7 \times 2 \times 27$ . Then, multiply the denominators together: $2 \times 1 \times 4$ .The multiplication of the numerators gives us $7 \times 2 \times 27 = 14 \times 27 = 378$ . The multiplication of the denominators gives us $2 \times 1 \times 4 = 8$ .
Round to Nearest Tenth: Simplify the multiplication. First, multiply the numerators together: $7 \times 2 \times 27$ . Then, multiply the denominators together: $2 \times 1 \times 4$ .The multiplication of the numerators gives us $7 \times 2 \times 27 = 14 \times 27 = 378$ . The multiplication of the denominators gives us $2 \times 1 \times 4 = 8$ .Now, divide the result from the numerators by the result from the denominators to get the volume in cubic inches: $\frac{378}{8}$ cubic inches.
Round to Nearest Tenth: Simplify the multiplication. First, multiply the numerators together: $7 \times 2 \times 27$ . Then, multiply the denominators together: $2 \times 1 \times 4$ .The multiplication of the numerators gives us $7 \times 2 \times 27 = 14 \times 27 = 378$ . The multiplication of the denominators gives us $2 \times 1 \times 4 = 8$ .Now, divide the result from the numerators by the result from the denominators to get the volume in cubic inches: $\frac{378}{8}$ cubic inches.To simplify $\frac{378}{8}$ , we perform the division. $378$ divided by $8$ equals $47.25$ cubic inches.
Round to Nearest Tenth: Simplify the multiplication. First, multiply the numerators together: $7 \times 2 \times 27$ . Then, multiply the denominators together: $2 \times 1 \times 4$ .The multiplication of the numerators gives us $7 \times 2 \times 27 = 14 \times 27 = 378$ . The multiplication of the denominators gives us $2 \times 1 \times 4 = 8$ .Now, divide the result from the numerators by the result from the denominators to get the volume in cubic inches: $\frac{378}{8}$ cubic inches.To simplify $\frac{378}{8}$ , we perform the division. $378$ divided by $8$ equals $47.25$ cubic inches.The question asks for the volume rounded to the nearest tenth. $47.25$ rounded to the nearest tenth is $2 \times 1 \times 4$ $0$ cubic inches.