Solve 90/360*3.14*(20sqrt{2})^2-200

$$\frac { 90 } { 360 } \times 3.14 \times ( 20 \sqrt { 2 } ) ^ { 2 } - 200$$

Evaluate

$$428$$

Solution Steps

Reduce the fraction \frac{90}{360} to lowest terms by extracting and canceling out 90.

$$3.14\times \frac{1}{4}\times \left(20\sqrt{2}\right)^{2}-200$$

Multiply 3.14 and \frac{1}{4} to get \frac{157}{200}.

$$\frac{157}{200}\times \left(20\sqrt{2}\right)^{2}-200$$

Expand \left(20\sqrt{2}\right)^{2}.

$$\frac{157}{200}\times 20^{2}\left(\sqrt{2}\right)^{2}-200$$

Calculate 20 to the power of 2 and get 400.

$$\frac{157}{200}\times 400\left(\sqrt{2}\right)^{2}-200$$

The square of \sqrt{2} is 2.

$$\frac{157}{200}\times 400\times 2-200$$

Multiply 400 and 2 to get 800.

$$\frac{157}{200}\times 800-200$$

Multiply \frac{157}{200} and 800 to get 628.

$$628-200$$

Subtract 200 from 628 to get 428.

$$428$$

Factor

$$107\times 2^{2}$$