Q.If the length, breadth, and height of a right rectangular prism are in the ratio 3:2:1 and its total surface area is 88 square centimeters, then what is its volume? (a) 120 cubic cm (b) 64 cubic cm (c) 48 cubic cm (d) 24 cubic cm
Answer: C
Let the length, breadth, and height of the right rectangular prism be \(3a\), \(2a\), and \(a\) respectively. \[ \therefore\ 2(3a \cdot 2a + 2a \cdot a + a \cdot 3a) = 88 \] i.e., \[ 2(6a^2 + 2a^2 + 3a^2) = 88 \] \[ 22a^2 = 88 \] \[ a^2 = 4 \] \[ a = 2 \] \(\therefore\) Volume = \(3a \cdot 2a \cdot a = 6a^3\) cubic cm \[ = 6 \times 2^3 = 6 \times 8 = 48\ \text{cubic cm} \]
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