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11 October, 03:01

A department store sells small boxes in which customers can store nails. The diagram below shows one of the boxes. The diagram is not drawn to scale. 2.54 cm, 14 cm, 8 cm. What are the lateral area and the surface area of the box to the nearest whole number? Use the large 14 cm times 8 cm rectangles on the top and bottom as the bases.

A) 112cm^2; 448cm^2

B) 112cm^2; 336cm^2

C) 56cm^2; 448cm^2

D) 56cm^2; 336cm^2

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  1. 11 October, 04:34
    0
    The answer is B) 112cm^2; 336cm^2.

    The lateral area (LA) is the product of the perimeter (P) of the base and the height (h):

    LA = Ph

    P = 2l + 2w = (2 x 14) + (2 x 8) = 28 + 16 = 44 cm

    LA = 44 cm x 2.54 cm = 112 cm²

    The surface area (SA) is the sum of all areas:

    SA = 2 (lw + wh + lh)

    SA = 2 ((14x8) + (8x2.54) + (14x2.54))

    SA = 2 (112 + 20.32 + 35.56)

    SA = 2 * 168

    SA = 336 cm²

    Thus, the lateral area and the surface area are 112 cm² and 336 cm², respectively.
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