Multiple Choice
A jewelry store buys small boxes in which to wrap items that they sell. The diagram below shows one of the boxes. Find the lateral area and the surface area of the box to the nearest whole number. Use the large 14 x 7 cm rectangles on the top and bottom as the bases.
A rectangular prism is shown. The height is 1.66 centimeters, the width is 7 centimeters, and the length is 14 centimeters.
(1 point)
Responses
35 cm2; 364 cm2
35 cm 2 ; 364 cm 2
70 cm2; 364 cm2
70 cm 2 ; 364 cm 2
35 cm2; 266 cm2
35 cm 2 ; 266 cm 2
70 cm2; 266 cm2
70 cm 2 ; 266 cm 2
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The lateral area of the box is equal to the sum of the areas of the four sides. The height of the box is 1.66 cm and the width and length are 7 cm and 14 cm respectively. Therefore, the lateral area is 2 * 1.66 * 7 + 2 * 1.66 * 14 = 32.94 cm².
The surface area of the box is equal to the sum of the areas of all six sides. In addition to the lateral area, we also need to consider the areas of the two bases. The area of each base is 14 * 7 = 98 cm². Therefore, the surface area is 32.94 + 98 + 98 = 228.94 cm².
Rounding to the nearest whole number, the lateral area is 33 cm² and the surface area is 229 cm².
Therefore, the correct answer is 35 cm²; 229 cm².