Solve 1/3(pi){left(5/6right)}^2(6/5)

$$\frac{ 1 }{ 3 } ( \pi ) { \left( \frac{ 5 }{ 6 } \right) }^{ 2 } ( \frac{ 6 }{ 5 } )$$

Evaluate

$$\frac{5\pi }{18}\approx 0.872664626$$

Solution Steps

Calculate \frac{5}{6} to the power of 2 and get \frac{25}{36}.

$$\frac{1}{3}\pi \times \frac{25}{36}\times \frac{6}{5}$$

Multiply \frac{1}{3} times \frac{25}{36} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 25}{3\times 36}\pi \times \frac{6}{5}$$

Do the multiplications in the fraction \frac{1\times 25}{3\times 36}.

$$\frac{25}{108}\pi \times \frac{6}{5}$$

Multiply \frac{25}{108} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25\times 6}{108\times 5}\pi$$

Do the multiplications in the fraction \frac{25\times 6}{108\times 5}.

$$\frac{150}{540}\pi$$

Reduce the fraction \frac{150}{540} to lowest terms by extracting and canceling out 30.

$$\frac{5}{18}\pi$$