Q.The length of a right rectangular prism is three times its width and five times its height. If its volume is 14,400 cubic centimeters, then what is its total surface area? (a) 4300 square cm (b) 4320 square cm (c) 4500 square cm (d) 4520 square cm
Answer Not Defined

Let the length of the rectangular prism be \(x\) cm. \[ \therefore \text{Width} = \frac{x}{3} \text{ cm}, \quad \text{Height} = \frac{x}{5} \text{ cm} \] \[ \therefore x \times \frac{x}{3} \times \frac{x}{5} = 14400 \Rightarrow \frac{x^3}{15} = 14400 \Rightarrow x^3 = 14400 \times 15 = 216000 \Rightarrow x = 60 \] \[ \therefore \text{Length} = 60 cm, \quad \text{Width} = \frac{60}{3} = 20 cm, \quad \text{Height} = \frac{60}{5} = 12 cm \] \[ \therefore \text{Total surface area} = 2(60 \times 20 + 20 \times 12 + 12 \times 60) \text{ cm}^2 = 2(1200 + 240 + 720) \text{ cm}^2 = 2 \times 2160 \text{ cm}^2 = 4320 \text{ cm}^2 \] \[ \therefore \text{The total surface area of the rectangular prism is } 4320 \text{ square cm}. \]
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