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A pyramid has a height of 11 cm. Its rectangular base has sides of length 10 cm and 7 cm. Calculate the volume of the pyramid.

Mathematics

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Answer

256.67 cm3\text{256.67 cm}^3

Step-by-step solution

4 steps

  1. Identify the given information and the shape.

    The figure shows a pyramid with apex A and base BCDE.
    The height of the pyramid is given as h=11 cmh = 11 \, \text{cm}.
    The base is a quadrilateral with side lengths CD=10 cmCD = 10 \, \text{cm} and ED=7 cmED = 7 \, \text{cm}. We will assume the base BCDE is a rectangle, with CDCD and EDED as its adjacent sides.

  2. Calculate the area of the base.

    For a rectangular base, the area is the product of its length and width.

    Base Area=CD×ED\text{Base Area} = CD \times ED Base Area=10 cm×7 cm\text{Base Area} = 10 \, \text{cm} \times 7 \, \text{cm} Base Area=70 cm2\text{Base Area} = 70 \, \text{cm}^2

  3. State the correct formula for the volume of a pyramid.

    The formula provided in the question, V=12×base area+heightV = \frac{1}{2} \times \text{base area} + \text{height}, is incorrect for calculating the volume of a pyramid. This formula would result in adding an area to a length, which does not yield a volume.
    The correct formula for the volume of a pyramid is:

    V=13×Base Area×heightV = \frac{1}{3} \times \text{Base Area} \times \text{height}

  4. Substitute the calculated base area and given height into the correct volume formula and compute the volume.

    V=13×70 cm2×11 cmV = \frac{1}{3} \times 70 \, \text{cm}^2 \times 11 \, \text{cm} V=7703 cm3V = \frac{770}{3} \, \text{cm}^3 V≈256.67 cm3V \approx 256.67 \, \text{cm}^3

    The volume of the pyramid is 256.67 cm3\text{256.67 cm}^3.

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