DIRECT AND INVERSE VARIATION CONTINUED - PUNJAB-BOARD / 10TH-CLASS / MATHEMATICS / 1-10-MATHS-FULL-10TH-CLASS-NBF-2024 / VARIATIONS / DIRECT-AND-INVERSE-VARIATION-CONTINUED

Given that $A$ varies directly as the square of $r$ and $A = \frac{1782}{7} {c m}^{2}$ , when $r = 9 c m$ .

If $r = 14 c m$ , then find $A$ .

Solution: Since $A$ varies directly as square of $r$

A \propto r^2

A = k r^2

\frac{1782}{7} = k (9)^{2}

\frac{1782}{7 \times 81} = k o r k = \frac{22}{7}

A = \frac{22}{7} (14)^{2} = \frac{22}{7} \times 14 \times 14 = 616 {c m}^{2}

If $y$ varies directly as cube of $x$ and $y = 81$ when $x = 3$ , so evaluate $y$ when $x = 5$ .

Solution: Given that $y$ varies directly as cube of $x$ .

i.e., $y\propto x^{3}$ or $y = kx^{3}$ (i) (where $k$ is constant)

Put $y = 81$ and $x = 3$ in (i)

81 = k (3)^{3} \Rightarrow 27 k = 81 \Rightarrow k = 3

Now put $k = 3$ and $x = 5$ in eq. (i)

y = 3(5)^3 = 375

3.1(c) Variations (Direct and Inverse) Continued