A) A slice of watermelon approximates the shape of a rectangular pyramid. Nicol's slice is 1 1 inch wide, 105 in. long, and 8 in. tall. What is the approximate volume of her watermelon slice? Round your answer to the nearest hundredth, if applicable. (1 point)

104.23 in.

205 in.

28 in.

84 in.

1 answer

The volume \( V \) of a rectangular pyramid can be calculated using the formula:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

For Nicol's slice of watermelon, we can determine the base area. The width of the slice is 1 inch, and the length is 105 inches. Therefore, the base area \( A \) is:

\[ A = \text{Width} \times \text{Length} = 1 , \text{in} \times 105 , \text{in} = 105 , \text{in}^2 \]

The height of the pyramid is given as 8 inches.

Now we can calculate the volume:

\[ V = \frac{1}{3} \times 105 , \text{in}^2 \times 8 , \text{in} \]

Calculating the multiplication first:

\[ 105 \times 8 = 840 , \text{in}^3 \]

Now, substituting back into the volume formula:

\[ V = \frac{1}{3} \times 840 , \text{in}^3 = 280 , \text{in}^3 \]

Therefore, the volume of Nicol's watermelon slice is approximately:

\[ \boxed{280} , \text{in}^3 \]

After checking your options, it seems like none of the provided options (104.23 in., 205 in., 28 in., 84 in.) matches with 280 in. However, if any mistake or confusion arises, please check if the dimensions provided are correctly noted or if there are any other aspects I might need to consider.