Tommy and Cole are planning to build a wooden toy chest. If the dimensions of the toy chest are 17 inches long, 9 inches wide, and 11 inches tall, how much wood will they need?

Surface Area of a Rectangular Prism: 2lw + 2lh + 2wh


(1 point)
Responses

504 square inches
504 square inches

1683 square inches
1683 square inches

878 square inches
878 square inches

37 square inches

1 answer

To find the amount of wood needed for the toy chest, we can calculate the surface area using the formula for the surface area of a rectangular prism:

\[ \text{Surface Area} = 2lw + 2lh + 2wh \]

where:

  • \( l \) is the length,
  • \( w \) is the width,
  • \( h \) is the height.

Given the dimensions:

  • \( l = 17 \) inches,
  • \( w = 9 \) inches,
  • \( h = 11 \) inches.

Now we can substitute these values into the formula.

  1. Calculate \( 2lw \): \[ 2lw = 2 \times 17 \times 9 = 306 \text{ square inches} \]

  2. Calculate \( 2lh \): \[ 2lh = 2 \times 17 \times 11 = 374 \text{ square inches} \]

  3. Calculate \( 2wh \): \[ 2wh = 2 \times 9 \times 11 = 198 \text{ square inches} \]

Now add these three areas together to find the total surface area:

\[ \text{Surface Area} = 306 + 374 + 198 = 878 \text{ square inches} \]

Thus, the amount of wood they will need is 878 square inches.

The correct response is:

878 square inches.