Solve 1/4*3.14*{left(15sqrt{2}right)}^2-15^2

$$\frac{ 1 }{ 4 } \times 3.14 \times { \left(15 \sqrt{ 2 } \right) }^{ 2 } - { 15 }^{ 2 }$$

Evaluate

$$128.25$$

Solution Steps

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

$$\frac{157}{200}\times \left(15\sqrt{2}\right)^{2}-15^{2}$$

Expand \left(15\sqrt{2}\right)^{2}.

$$\frac{157}{200}\times 15^{2}\left(\sqrt{2}\right)^{2}-15^{2}$$

Calculate 15 to the power of 2 and get 225.

$$\frac{157}{200}\times 225\left(\sqrt{2}\right)^{2}-15^{2}$$

The square of \sqrt{2} is 2.

$$\frac{157}{200}\times 225\times 2-15^{2}$$

Multiply 225 and 2 to get 450.

$$\frac{157}{200}\times 450-15^{2}$$

Multiply \frac{157}{200} and 450 to get \frac{1413}{4}.

$$\frac{1413}{4}-15^{2}$$

Calculate 15 to the power of 2 and get 225.

$$\frac{1413}{4}-225$$

Subtract 225 from \frac{1413}{4} to get \frac{513}{4}.

$$\frac{513}{4}$$

Factor

$$\frac{19 \cdot 3 ^ {3}}{2 ^ {2}} = 128\frac{1}{4} = 128.25$$