26 A right rectangular prism has a base area of 24t squarecentimeters cm^2. The length of the base ^ 8 of the rectangular prism is h/3 cm, and the height of the rectangular prism is 15cm. Which expression represents the surface area, in cm^2, of the right rectangular prism? +
Correct answer: B (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice B is correct. It’s given that the base area of the right rectangular prism is 24 cm2 8 cm t and the length of the base is 3 . Dividing the base area by the length 2 8 4 t 24 3 9 cm yields the width: 3 , or ^ tha8k, or t . It’s also given that the height of the 15cm prism is . A right rectangular prism has two rectangular bases and four 2 24 48 cm2 rectangular lateral faces. The total area of the t 8 wo bases is ^ th, or t . The cm 15cm four lateral faces include two with dimensions 3 by and two with 9 cm 15cm dimensions t by . The total area of these four lateral faces is 2 8 15 +2 9 15 cm2 80+270 cm2 a3k^ h ^ th^ h , which is equivalent to t . Adding this to the 48 +270 +80 318 +80cm2 total area of the two bases yields t t , or t . Thus, the cm2 expression, which represents the surface area, in , of the right rectangular 318 +80 prism is t . Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. cm3 cm2 Choice D is incorrect. This is the volume, in , not the surface area, in .
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