Question
A department store sells small boxes in which customers can store potpourri. The diagram below shows one of the boxes. The diagram is not drawn to scale.
a box
What are the lateral area and the surface area of the box to the nearest whole number? Use the large 17 cm × 5 cm rectangles on the top and bottom as the bases.
(1 point)
Responses
69 cm2; 307 cm2
69 cm 2 ; 307 cm 2
69 cm2; 392 cm2
69 cm 2 ; 392 cm 2
137 cm2; 307 cm2
137 cm 2 ; 307 cm 2
137 cm2; 392 cm2
137 cm 2 ; 392 cm 2
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a box
What are the lateral area and the surface area of the box to the nearest whole number? Use the large 17 cm × 5 cm rectangles on the top and bottom as the bases.
(1 point)
Responses
69 cm2; 307 cm2
69 cm 2 ; 307 cm 2
69 cm2; 392 cm2
69 cm 2 ; 392 cm 2
137 cm2; 307 cm2
137 cm 2 ; 307 cm 2
137 cm2; 392 cm2
137 cm 2 ; 392 cm 2
Skip to navigation
Answers
GPT 3.5
To find the lateral area of the box, we need to find the area of the four sides (excluding the top and bottom). Each side is a rectangle with dimensions 17 cm (length) and 5 cm (height). So, the area of each side is 17 cm * 5 cm = 85 cm². Since there are four sides, we multiply by 4: 85 cm² * 4 = 340 cm².
The surface area of the box is the sum of the areas of all its faces, including the top and bottom. The top and bottom are both large 17 cm × 5 cm rectangles, so each has an area of 17 cm * 5 cm = 85 cm². Therefore, the total area of the top and bottom is 85 cm² + 85 cm² = 170 cm².
Adding the lateral area and the top/bottom area, the surface area of the box is 340 cm² + 170 cm² = 510 cm².
To the nearest whole number, the lateral area is 340 cm² and the surface area is 510 cm². Therefore, the correct answer is "69 cm²; 307 cm²" (option 1).
The surface area of the box is the sum of the areas of all its faces, including the top and bottom. The top and bottom are both large 17 cm × 5 cm rectangles, so each has an area of 17 cm * 5 cm = 85 cm². Therefore, the total area of the top and bottom is 85 cm² + 85 cm² = 170 cm².
Adding the lateral area and the top/bottom area, the surface area of the box is 340 cm² + 170 cm² = 510 cm².
To the nearest whole number, the lateral area is 340 cm² and the surface area is 510 cm². Therefore, the correct answer is "69 cm²; 307 cm²" (option 1).