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The image shows a rectangular prism with dimensions labeled as 1cm, 1cm, and 14cm. What is the volume of this prism?

Mathematics

ScanSolve AI Answer

Answer

58 cm258 \text{ cm}^2

Step-by-step solution

3 steps

To find the surface area of the rectangular prism, we need to sum the areas of all its faces.

  1. Identify the dimensions of the rectangular prism.

    From the image, we can identify the following dimensions:

    • Length, l=14 cml = 14 \text{ cm}.
    • Width, w=1 cmw = 1 \text{ cm}.
    • Height, h=1 cmh = 1 \text{ cm}.
  2. Calculate the area of each pair of identical faces.

    A rectangular prism has three pairs of identical faces:

    • Two faces with dimensions l×wl \times w: 2×(14 cm×1 cm)=2×14 cm2=28 cm22 \times (14 \text{ cm} \times 1 \text{ cm}) = 2 \times 14 \text{ cm}^2 = 28 \text{ cm}^2.
    • Two faces with dimensions l×hl \times h: 2×(14 cm×1 cm)=2×14 cm2=28 cm22 \times (14 \text{ cm} \times 1 \text{ cm}) = 2 \times 14 \text{ cm}^2 = 28 \text{ cm}^2.
    • Two faces with dimensions w×hw \times h: 2×(1 cm×1 cm)=2×1 cm2=2 cm22 \times (1 \text{ cm} \times 1 \text{ cm}) = 2 \times 1 \text{ cm}^2 = 2 \text{ cm}^2.
  3. Calculate the total surface area.

    The total surface area (SASA) is the sum of the areas of all six faces.

    SA=2(lw+lh+wh)SA = 2(lw + lh + wh) SA=2(14 cm×1 cm+14 cm×1 cm+1 cm×1 cm)SA = 2(14 \text{ cm} \times 1 \text{ cm} + 14 \text{ cm} \times 1 \text{ cm} + 1 \text{ cm} \times 1 \text{ cm}) SA=2(14 cm2+14 cm2+1 cm2)SA = 2(14 \text{ cm}^2 + 14 \text{ cm}^2 + 1 \text{ cm}^2) SA=2(29 cm2)SA = 2(29 \text{ cm}^2) SA=58 cm2SA = 58 \text{ cm}^2

    The final answer is 58 cm258 \text{ cm}^2.

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