uestion 3 The volume of a water tank is \( V=h \times b \times l \) cube metres \( \left(m^{3}\right) \), where \( l \) is length, \( b \) is base and \( h \) is height. If the height of the water tank is \( 3 x \), the length is \( 2 x \) and the base is \( 3 x+4 \), what is the volume of the water tank in terms of \( x \)

To find the volume of the water tank in terms of \( x \), we can substitute the given dimensions into the volume formula \( V = h \times b \times l \). Given: - Height \( h = 3x \) - Length \( l = 2x \) - Base \( b = 3x + 4 \) Now, we can substitute these values into the volume formula: \[ V = h \times b \times l \] Substituting the values: \[ V = (3x) \times (3x + 4) \times (2x) \] Now, we can simplify this expression step by step. First, calculate \( (3x) \times (2x) \): \[ (3x) \times (2x) = 6x^2 \] Now, we can multiply this result by \( (3x + 4) \): \[ V = 6x^2 \times (3x + 4) \] Distributing \( 6x^2 \): \[ V = 6x^2 \times 3x + 6x^2 \times 4 \] Calculating each term: \[ V = 18x^3 + 24x^2 \] Thus, the volume of the water tank in terms of \( x \) is: \[ \boxed{18x^3 + 24x^2} \]