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

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

Evaluate

$$108$$

Solution Steps

Cancel out \pi in both numerator and denominator.

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

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.

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

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

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

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

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

Divide 84 by 6 to get 14.

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

Multiply 14 and 10.5 to get 147.

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

Multiply 147 and 10.5 to get 1543.5.

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

Convert decimal number 3.5 to fraction \frac{35}{10}. Reduce the fraction \frac{35}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1543.5}{\frac{1}{3}\times \frac{7}{2}\times 3.5\times 3.5}$$

Multiply \frac{1}{3} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1543.5}{\frac{1\times 7}{3\times 2}\times 3.5\times 3.5}$$

Do the multiplications in the fraction \frac{1\times 7}{3\times 2}.

$$\frac{1543.5}{\frac{7}{6}\times 3.5\times 3.5}$$

Convert decimal number 3.5 to fraction \frac{35}{10}. Reduce the fraction \frac{35}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1543.5}{\frac{7}{6}\times \frac{7}{2}\times 3.5}$$

Multiply \frac{7}{6} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1543.5}{\frac{7\times 7}{6\times 2}\times 3.5}$$

Do the multiplications in the fraction \frac{7\times 7}{6\times 2}.

$$\frac{1543.5}{\frac{49}{12}\times 3.5}$$

Convert decimal number 3.5 to fraction \frac{35}{10}. Reduce the fraction \frac{35}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1543.5}{\frac{49}{12}\times \frac{7}{2}}$$

Multiply \frac{49}{12} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1543.5}{\frac{49\times 7}{12\times 2}}$$

Do the multiplications in the fraction \frac{49\times 7}{12\times 2}.

$$\frac{1543.5}{\frac{343}{24}}$$

Divide 1543.5 by \frac{343}{24} by multiplying 1543.5 by the reciprocal of \frac{343}{24}.

$$1543.5\times \frac{24}{343}$$

Convert decimal number 1543.5 to fraction \frac{15435}{10}. Reduce the fraction \frac{15435}{10} to lowest terms by extracting and canceling out 5.

$$\frac{3087}{2}\times \frac{24}{343}$$

Multiply \frac{3087}{2} times \frac{24}{343} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3087\times 24}{2\times 343}$$

Do the multiplications in the fraction \frac{3087\times 24}{2\times 343}.

$$\frac{74088}{686}$$

Divide 74088 by 686 to get 108.

$$108$$

Factor

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