(792)/(7)=(4)/(3)×(22)/(7)×r^(3).

Write Equation: Write down the given equation. The given equation is (792)/(7)=(4)/(3)×(22)/(7)×r^(3).Simplify Right Side: Simplify the right side of the equation by multiplying the fractions. (4)/(3)×(22)/(7) = (4×22)/(3×7) = (88)/(21). So, the equation becomes (792)/(7)=(88)/(21)×r^(3).Multiply by 7: Multiply both sides of the equation by 7 to eliminate the denominator on the left side. (792)/(7)×7 = (88)/(21)×r^(3)×7. This simplifies to 792 = (88×7)/(21)×r^(3).Calculate Value: Calculate the value of 88×7. 88×7 = 616. So, the equation now is 792 = (616)/(21)×r^(3).Divide by Fraction: Divide both sides of the equation by (616)/(21) to solve for r^(3). 792 ÷ (616)/(21) = r^(3).Calculate Value: Calculate the value of 792 ÷ (616)/(21). To divide by a fraction, multiply by its reciprocal. So, we multiply 792 by (21)/(616). 792 × (21)/(616) = r^(3).Simplify Fraction: Calculate the value of 792 × (21)/(616). 792 × (21)/(616) = 16632/616.Take Cube Root: Simplify the fraction 16632/616. 16632/616 = 27. So, the equation now is 27 = r^(3).Calculate Cube Root: Take the cube root of both sides to solve for r. r = ³√27.Calculate the cube root of 27. ³√27 = 3. So, r = 3.

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$\frac{792}{7}=\frac{4}{3} \times \frac{22}{7} \times r^{3}$ .

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\frac{792}{7}=\frac{4}{3} \times \frac{22}{7} \times r^{3}

Write Equation: Write down the given equation. $\newline$ The given equation is $\frac{792}{7}=\frac{4}{3}\times\frac{22}{7}\times r^{3}$ .
Simplify Right Side: Simplify the right side of the equation by multiplying the fractions. $\newline$ $(\frac{4}{3})\times(\frac{22}{7}) = (\frac{4\times22}{3\times7}) = (\frac{88}{21})$ . $\newline$ So, the equation becomes $(\frac{792}{7})=(\frac{88}{21})\times r^{3}$ .
Multiply by $7$ : Multiply both sides of the equation by $7$ to eliminate the denominator on the left side. $\newline$ $\frac{792}{7}\times7 = \frac{88}{21}\times r^{3}\times7$ . $\newline$ This simplifies to $792 = \frac{88\times7}{21}\times r^{3}$ .
Calculate Value: Calculate the value of $88\times7$ . $\newline$ $88\times7 = 616$ . $\newline$ So, the equation now is $792 = \frac{616}{21}\times r^{3}$ .
Divide by Fraction: Divide both sides of the equation by $(616)/(21)$ to solve for $r^{3}$ . $792 \div (616)/(21) = r^{3}$ .
Calculate Value: Calculate the value of $792 \div \left(\frac{616}{21}\right)$ . To divide by a fraction, multiply by its reciprocal. So, we multiply $792$ by $\left(\frac{21}{616}\right)$ . $792 \times \left(\frac{21}{616}\right) = r^{3}$ .
Simplify Fraction: Calculate the value of $792 \times \frac{21}{616}$ . $\newline$ $792 \times \frac{21}{616} = \frac{16632}{616}$ .
Take Cube Root: Simplify the fraction $\frac{16632}{616}$ . $\frac{16632}{616} = 27$ . So, the equation now is $27 = r^{3}$ .
Calculate Cube Root: Take the cube root of both sides to solve for $r$ . $r = \sqrt[3]{27}.$
Calculate Cube Root: Take the cube root of both sides to solve for $r$ . $r = \sqrt[3]{27}$ .Calculate the cube root of $27$ . $\sqrt[3]{27} = 3$ .So, $r = 3$ .