Solve =0.425*pi^2*200000/12*(1-0.3^2)(1/37.6)^2

$$= \frac { 0.425 \times \pi ^ { 2 } \times 200000 } { 12 \times ( 1 - 0.3 ^ { 2 } ) } ( \frac { 1 } { 37.6 } ) ^ { 2 }$$

Evaluate

$$\frac{6640625\pi ^{2}}{1206114}\approx 54.340088686$$

Solution Steps

Cancel out 4 in both numerator and denominator.

$$\frac{0.425\times 50000\pi ^{2}}{3\left(1-0.3^{2}\right)}\times \left(\frac{1}{37.6}\right)^{2}$$

Multiply 0.425 and 50000 to get 21250.

$$\frac{21250\pi ^{2}}{3\left(1-0.3^{2}\right)}\times \left(\frac{1}{37.6}\right)^{2}$$

Calculate 0.3 to the power of 2 and get 0.09.

$$\frac{21250\pi ^{2}}{3\left(1-0.09\right)}\times \left(\frac{1}{37.6}\right)^{2}$$

Subtract 0.09 from 1 to get 0.91.

$$\frac{21250\pi ^{2}}{3\times 0.91}\times \left(\frac{1}{37.6}\right)^{2}$$

Multiply 3 and 0.91 to get 2.73.

$$\frac{21250\pi ^{2}}{2.73}\times \left(\frac{1}{37.6}\right)^{2}$$

Divide 21250\pi ^{2} by 2.73 to get \frac{2125000}{273}\pi ^{2}.

$$\frac{2125000}{273}\pi ^{2}\times \left(\frac{1}{37.6}\right)^{2}$$

Expand \frac{1}{37.6} by multiplying both numerator and the denominator by 10.

$$\frac{2125000}{273}\pi ^{2}\times \left(\frac{10}{376}\right)^{2}$$

Reduce the fraction \frac{10}{376} to lowest terms by extracting and canceling out 2.

$$\frac{2125000}{273}\pi ^{2}\times \left(\frac{5}{188}\right)^{2}$$

Calculate \frac{5}{188} to the power of 2 and get \frac{25}{35344}.

$$\frac{2125000}{273}\pi ^{2}\times \frac{25}{35344}$$

Multiply \frac{2125000}{273} and \frac{25}{35344} to get \frac{6640625}{1206114}.

$$\frac{6640625}{1206114}\pi ^{2}$$

Expand

$$\frac{6640625 \pi ^ {2}}{1206114} = 54.34008868646249$$

Solution Steps

Cancel out 4 in both numerator and denominator.

$$\frac{0.425\times 50000\pi ^{2}}{3\left(1-0.3^{2}\right)}\times \left(\frac{1}{37.6}\right)^{2}$$

Multiply 0.425 and 50000 to get 21250.

$$\frac{21250\pi ^{2}}{3\left(1-0.3^{2}\right)}\times \left(\frac{1}{37.6}\right)^{2}$$

Calculate 0.3 to the power of 2 and get 0.09.

$$\frac{21250\pi ^{2}}{3\left(1-0.09\right)}\times \left(\frac{1}{37.6}\right)^{2}$$

Subtract 0.09 from 1 to get 0.91.

$$\frac{21250\pi ^{2}}{3\times 0.91}\times \left(\frac{1}{37.6}\right)^{2}$$

Multiply 3 and 0.91 to get 2.73.

$$\frac{21250\pi ^{2}}{2.73}\times \left(\frac{1}{37.6}\right)^{2}$$

Divide 21250\pi ^{2} by 2.73 to get \frac{2125000}{273}\pi ^{2}.

$$\frac{2125000}{273}\pi ^{2}\times \left(\frac{1}{37.6}\right)^{2}$$

Expand \frac{1}{37.6} by multiplying both numerator and the denominator by 10.

$$\frac{2125000}{273}\pi ^{2}\times \left(\frac{10}{376}\right)^{2}$$

Reduce the fraction \frac{10}{376} to lowest terms by extracting and canceling out 2.

$$\frac{2125000}{273}\pi ^{2}\times \left(\frac{5}{188}\right)^{2}$$

Calculate \frac{5}{188} to the power of 2 and get \frac{25}{35344}.

$$\frac{2125000}{273}\pi ^{2}\times \frac{25}{35344}$$

Multiply \frac{2125000}{273} and \frac{25}{35344} to get \frac{6640625}{1206114}.

$$\frac{6640625}{1206114}\pi ^{2}$$