Solve 10/3pi(5.4)^2-10/3pi(5)^2/0.4

$$\frac { \frac { 10 } { 3 } \pi ( 5.4 ) ^ { 2 } - \frac { 10 } { 3 } \pi ( 5 ) ^ { 2 } } { 0.4 }$$

Evaluate

$$\frac{104\pi }{3}\approx 108.908545324$$

Solution Steps

Calculate 5.4 to the power of 2 and get 29.16.

$$\frac{\frac{10}{3}\pi \times 29.16-\frac{10}{3}\pi \times 5^{2}}{0.4}$$

Convert decimal number 29.16 to fraction \frac{2916}{100}. Reduce the fraction \frac{2916}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{10}{3}\pi \times \frac{729}{25}-\frac{10}{3}\pi \times 5^{2}}{0.4}$$

Multiply \frac{10}{3} times \frac{729}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{10\times 729}{3\times 25}\pi -\frac{10}{3}\pi \times 5^{2}}{0.4}$$

Do the multiplications in the fraction \frac{10\times 729}{3\times 25}.

$$\frac{\frac{7290}{75}\pi -\frac{10}{3}\pi \times 5^{2}}{0.4}$$

Reduce the fraction \frac{7290}{75} to lowest terms by extracting and canceling out 15.

$$\frac{\frac{486}{5}\pi -\frac{10}{3}\pi \times 5^{2}}{0.4}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\frac{486}{5}\pi -\frac{10}{3}\pi \times 25}{0.4}$$

Express \frac{10}{3}\times 25 as a single fraction.

$$\frac{\frac{486}{5}\pi -\frac{10\times 25}{3}\pi }{0.4}$$

Multiply 10 and 25 to get 250.

$$\frac{\frac{486}{5}\pi -\frac{250}{3}\pi }{0.4}$$

Combine \frac{486}{5}\pi and -\frac{250}{3}\pi to get \frac{208}{15}\pi .

$$\frac{\frac{208}{15}\pi }{0.4}$$

Divide \frac{208}{15}\pi by 0.4 to get \frac{104}{3}\pi .

$$\frac{104}{3}\pi$$

Expand

$$\frac{104 \pi}{3} = 108.90854532444617$$

Solution Steps

Calculate 5.4 to the power of 2 and get 29.16.

$$\frac{\frac{10}{3}\pi \times 29.16-\frac{10}{3}\pi \times 5^{2}}{0.4}$$

Convert decimal number 29.16 to fraction \frac{2916}{100}. Reduce the fraction \frac{2916}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{10}{3}\pi \times \frac{729}{25}-\frac{10}{3}\pi \times 5^{2}}{0.4}$$

Multiply \frac{10}{3} times \frac{729}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{10\times 729}{3\times 25}\pi -\frac{10}{3}\pi \times 5^{2}}{0.4}$$

Do the multiplications in the fraction \frac{10\times 729}{3\times 25}.

$$\frac{\frac{7290}{75}\pi -\frac{10}{3}\pi \times 5^{2}}{0.4}$$

Reduce the fraction \frac{7290}{75} to lowest terms by extracting and canceling out 15.

$$\frac{\frac{486}{5}\pi -\frac{10}{3}\pi \times 5^{2}}{0.4}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\frac{486}{5}\pi -\frac{10}{3}\pi \times 25}{0.4}$$

Express \frac{10}{3}\times 25 as a single fraction.

$$\frac{\frac{486}{5}\pi -\frac{10\times 25}{3}\pi }{0.4}$$

Multiply 10 and 25 to get 250.

$$\frac{\frac{486}{5}\pi -\frac{250}{3}\pi }{0.4}$$

Combine \frac{486}{5}\pi and -\frac{250}{3}\pi to get \frac{208}{15}\pi .

$$\frac{\frac{208}{15}\pi }{0.4}$$

Divide \frac{208}{15}\pi by 0.4 to get \frac{104}{3}\pi .

$$\frac{104}{3}\pi$$