Solve frac{90pi{left(sqrt{6^2+1^2}right)}^2}{360}-frac{90*pi{left(sqrt{4^2+2^2}right)}^2}{360}

$$\frac{ 90 \pi { \left( \sqrt{ { 6 }^{ 2 } + { 1 }^{ 2 } } \right) }^{ 2 } }{ 360 } - \frac{ 90 \times \pi { \left( \sqrt{ { 4 }^{ 2 } + { 2 }^{ 2 } } \right) }^{ 2 } }{ 360 }$$

Evaluate

$$\frac{17\pi }{4}\approx 13.351768778$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$\frac{90\pi \left(\sqrt{36+1^{2}}\right)^{2}}{360}-\frac{90\pi \left(\sqrt{4^{2}+2^{2}}\right)^{2}}{360}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{90\pi \left(\sqrt{36+1}\right)^{2}}{360}-\frac{90\pi \left(\sqrt{4^{2}+2^{2}}\right)^{2}}{360}$$

Add 36 and 1 to get 37.

$$\frac{90\pi \left(\sqrt{37}\right)^{2}}{360}-\frac{90\pi \left(\sqrt{4^{2}+2^{2}}\right)^{2}}{360}$$

The square of \sqrt{37} is 37.

$$\frac{90\pi \times 37}{360}-\frac{90\pi \left(\sqrt{4^{2}+2^{2}}\right)^{2}}{360}$$

Multiply 90 and 37 to get 3330.

$$\frac{3330\pi }{360}-\frac{90\pi \left(\sqrt{4^{2}+2^{2}}\right)^{2}}{360}$$

Divide 3330\pi by 360 to get \frac{37}{4}\pi .

$$\frac{37}{4}\pi -\frac{90\pi \left(\sqrt{4^{2}+2^{2}}\right)^{2}}{360}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{37}{4}\pi -\frac{90\pi \left(\sqrt{16+2^{2}}\right)^{2}}{360}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{37}{4}\pi -\frac{90\pi \left(\sqrt{16+4}\right)^{2}}{360}$$

Add 16 and 4 to get 20.

$$\frac{37}{4}\pi -\frac{90\pi \left(\sqrt{20}\right)^{2}}{360}$$

The square of \sqrt{20} is 20.

$$\frac{37}{4}\pi -\frac{90\pi \times 20}{360}$$

Multiply 90 and 20 to get 1800.

$$\frac{37}{4}\pi -\frac{1800\pi }{360}$$

Divide 1800\pi by 360 to get 5\pi .

$$\frac{37}{4}\pi -5\pi$$

Combine \frac{37}{4}\pi and -5\pi to get \frac{17}{4}\pi .

$$\frac{17}{4}\pi$$