Solve 1/3*3.14*5^2-1/3*3.14*4^2

$$\frac { 1 } { 3 } \times 3.14 \times 5 ^ { 2 } - \frac { 1 } { 3 } \times 3.14 \times 4 ^ { 2 }$$

Evaluate

$$9.42$$

Solution Steps

Convert decimal number 3.14 to fraction \frac{314}{100}. Reduce the fraction \frac{314}{100} to lowest terms by extracting and canceling out 2.

$$\frac{1}{3}\times \frac{157}{50}\times 5^{2}-\frac{1}{3}\times 3.14\times 4^{2}$$

Multiply \frac{1}{3} times \frac{157}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 157}{3\times 50}\times 5^{2}-\frac{1}{3}\times 3.14\times 4^{2}$$

Do the multiplications in the fraction \frac{1\times 157}{3\times 50}.

$$\frac{157}{150}\times 5^{2}-\frac{1}{3}\times 3.14\times 4^{2}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{157}{150}\times 25-\frac{1}{3}\times 3.14\times 4^{2}$$

Express \frac{157}{150}\times 25 as a single fraction.

$$\frac{157\times 25}{150}-\frac{1}{3}\times 3.14\times 4^{2}$$

Multiply 157 and 25 to get 3925.

$$\frac{3925}{150}-\frac{1}{3}\times 3.14\times 4^{2}$$

Reduce the fraction \frac{3925}{150} to lowest terms by extracting and canceling out 25.

$$\frac{157}{6}-\frac{1}{3}\times 3.14\times 4^{2}$$

Convert decimal number 3.14 to fraction \frac{314}{100}. Reduce the fraction \frac{314}{100} to lowest terms by extracting and canceling out 2.

$$\frac{157}{6}-\frac{1}{3}\times \frac{157}{50}\times 4^{2}$$

Multiply \frac{1}{3} times \frac{157}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{157}{6}-\frac{1\times 157}{3\times 50}\times 4^{2}$$

Do the multiplications in the fraction \frac{1\times 157}{3\times 50}.

$$\frac{157}{6}-\frac{157}{150}\times 4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{157}{6}-\frac{157}{150}\times 16$$

Express \frac{157}{150}\times 16 as a single fraction.

$$\frac{157}{6}-\frac{157\times 16}{150}$$

Multiply 157 and 16 to get 2512.

$$\frac{157}{6}-\frac{2512}{150}$$

Reduce the fraction \frac{2512}{150} to lowest terms by extracting and canceling out 2.

$$\frac{157}{6}-\frac{1256}{75}$$

Least common multiple of 6 and 75 is 150. Convert \frac{157}{6} and \frac{1256}{75} to fractions with denominator 150.

$$\frac{3925}{150}-\frac{2512}{150}$$

Since \frac{3925}{150} and \frac{2512}{150} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3925-2512}{150}$$

Subtract 2512 from 3925 to get 1413.

$$\frac{1413}{150}$$

Reduce the fraction \frac{1413}{150} to lowest terms by extracting and canceling out 3.

$$\frac{471}{50}$$

Factor

$$\frac{3 \cdot 157}{2 \cdot 5 ^ {2}} = 9\frac{21}{50} = 9.42$$