Mathematics

Question

The altitude of the regular quadrilateral prism is h=13 cm and lateral area is AL = 624 cm2. Find: 1) The Surface Area of the prism; 2) The Volume of the prism.

1. The Surface Area is equal to
cm2
2. The Volume is equal to
cm3

2 Answer

  • Lateral area: AL = 4 * s * h
    624 = 4 * s * 13
    624 = 52 s
    s = 624 : 52
    s = 12 cm
    The surface area of the prism:
    A = 2 ·12² + 624
    A = 2 · 144 + 624 = 288 + 624 =912 cm²
    The volume:
    V = a² · h = 12² · 13 = 144 · 13 = 1,872 cm³
    Answer:
    1. The surface area is equal to 912 cm².
    2. The volume is equal to 1,872 cm³.

  • A regular quadrilateral prism has 4 lateral sides, all congruent. The figures are: Surface area of the prism = 7106 sq. cm., Volume of the prism =  29952 cubic cm.

    How to find volume of a right prism?

    Volume of a right prism = Bh cubic units, where B is the Base's area and h is its height.

    Since a regular quadrilateral prism has 4 congruent lateral sides, its lateral surface area is 4 times 624 = 2496 sq. cm.

    Let its base area be B. Since the prism has got 13 inch height, it is one of the side of the lateral rectangles.

    Since area of rectangle = product of two adjacent sides' lengths

    624 = x times 13, x = 48 cms

    This x is side of the base of that prism. Know that in a regular quadrilateral prism, due to symmetry(regularity), there is base as a square. Its side length is another side of those lateral rectangles as one side is used as height, thus, base square's side length = x = 48 cms.

    Base area = B = square of 48 = 2304 sq. cm.

    Thus,

    Total surface area of prism = 2 times base + lateral area( as top + bottom + lateral sides make up the surface of that prism, and top is symmetric to bottom due to prism being regular)

    Total surface area = 4608 + 2496 = 7106 sq. cm.

    Volume of prism = B times h = 2304 times 13 = 29952 cubic cm.

    Thus,

    The figures are:

    • Surface area of the prism = 7106 sq. cm.,
    • Volume of the prism =  29952 cubic cm.

    Learn more about volume of right prism here:

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