Identify given parameters

We are given the radius $r = 7$ cm and the constant $\pi = \frac{22}{7}$.

$r = 7, \pi = \frac{22}{7}$

Apply volume formula

Substitute the values into the sphere volume formula: $V = \frac{4}{3} \pi r^3$.

$V = \frac{4}{3} \times \frac{22}{7} \times 7^3$

Simplify calculation

Simplify the expression by canceling one $7$ from the denominator: $V = \frac{4}{3} \times 22 \times 7^2 = \frac{4 \times 22 \times 49}{3}$.

$V = \frac{88 \times 49}{3} = \frac{4312}{3}$

Final division

Calculate the final quotient: $4312 \div 3 = 1437.333...$ cm$^3$.

$V \approx 1437.33 \text{ cm}^3$