Q.The dimensions of a right rectangular prism are in the ratio 6:5:4. If its total surface area is 3700 square centimeters, what is its volume in cubic centimeters? (a) 1500 cubic cm (b) 51000 cubic cm (c) 50100 cubic cm (d) 15000 cubic cm
Answer: D
Assume the dimensions of the right rectangular prism are \(6a, 5a, 4a\). Therefore, \[ 2(6a \cdot 5a + 5a \cdot 4a + 4a \cdot 6a) = 3700 \] Or, \[ 2(30a^2 + 20a^2 + 24a^2) = 3700 \] Or, \[ 148a^2 = 3700 \] So, \[ a^2 = 25 \] Thus, \[ a = 5 \] Therefore, the volume is: \[ 6a \cdot 5a \cdot 4a = 120a^3 \text{ cubic cm} \] \[ = 120 \times 5^3 \text{ cubic cm} \] \[ = 120 \times 125 \text{ cubic cm} \] \[ = 15000 \text{ cubic cm} \]
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