Subjects algebra

Volume Expressions 96F888

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1. **State the problem:** We need to find the volume of solids formed by multiplying length ($l$), breadth ($b$), and height ($h$) for each given shape. 2. **Formula:** Volume $= l \times b \times h$ 3. **Given:** For each shape, we have dimensions labeled as algebraic expressions. We assume height $h=1$ unless otherwise specified, since only two dimensions are given for some shapes. 4. **Calculate volumes:** **a)** Rectangle with width $a=x$, length $b=7$, height $h=1$: $$V_a = x \times 7 \times 1 = 7x$$ **b)** Square with sides $a=x$, so length $l=x$, breadth $b=x$, height $h=1$: $$V_b = x \times x \times 1 = x^2$$ **c)** Rectangle with width $3$, length $x$, height $1$: $$V_c = 3 \times x \times 1 = 3x$$ **d)** Rectangle with width $5x + 3$, length $1$, height $1$: $$V_d = (5x + 3) \times 1 \times 1 = 5x + 3$$ **e)** Rectangle with width $x + 7$, length $1$, height $1$: $$V_e = (x + 7) \times 1 \times 1 = x + 7$$ 5. **Summary:** - Volume a) $7x$ - Volume b) $x^2$ - Volume c) $3x$ - Volume d) $5x + 3$ - Volume e) $x + 7$ Each volume is expressed as an algebraic expression in terms of $x$.