Solve 4/3pi*10.5*10.5*10.5/frac{1{3}pi*3.5*3.5*3}

$$\frac { \frac { 4 } { 3 } \pi \times 10.5 \times 10.5 \times 10.5 } { \frac { 1 } { 3 } \pi \times 3.5 \times 3.5 \times 3 }$$

Evaluate

$$126$$

Solution Steps

Cancel out \pi in both numerator and denominator.

$$\frac{\frac{4}{3}\times 10.5\times 10.5\times 10.5}{\frac{1}{3}\times 3\times 3.5\times 3.5}$$

Convert decimal number 10.5 to fraction \frac{105}{10}. Reduce the fraction \frac{105}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{4}{3}\times \frac{21}{2}\times 10.5\times 10.5}{\frac{1}{3}\times 3\times 3.5\times 3.5}$$

Multiply \frac{4}{3} times \frac{21}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{4\times 21}{3\times 2}\times 10.5\times 10.5}{\frac{1}{3}\times 3\times 3.5\times 3.5}$$

Do the multiplications in the fraction \frac{4\times 21}{3\times 2}.

$$\frac{\frac{84}{6}\times 10.5\times 10.5}{\frac{1}{3}\times 3\times 3.5\times 3.5}$$

Divide 84 by 6 to get 14.

$$\frac{14\times 10.5\times 10.5}{\frac{1}{3}\times 3\times 3.5\times 3.5}$$

Multiply 14 and 10.5 to get 147.

$$\frac{147\times 10.5}{\frac{1}{3}\times 3\times 3.5\times 3.5}$$

Multiply 147 and 10.5 to get 1543.5.

$$\frac{1543.5}{\frac{1}{3}\times 3\times 3.5\times 3.5}$$

Cancel out 3 and 3.

$$\frac{1543.5}{3.5\times 3.5}$$

Multiply 3.5 and 3.5 to get 12.25.

$$\frac{1543.5}{12.25}$$

Expand \frac{1543.5}{12.25} by multiplying both numerator and the denominator by 100.

$$\frac{154350}{1225}$$

Divide 154350 by 1225 to get 126.

$$126$$

Factor

$$2\times 7\times 3^{2}$$