Solve 4*pi^2*left(2.28*10^8right)^3divleft(687*24*60*60right)^2/3.72*{6794^2div4}

$$\frac{ 4 \times { \pi }^{ 2 } \times { \left(2.28 \times { 10 }^{ 8 } \right) }^{ 3 } \div { \left(687 \times 24 \times 60 \times 60 \right) }^{ 2 } }{ 3.72 \times { 6794 }^{ 2 } \div 4 }$$

Evaluate

$$\frac{4286875000000000000\pi ^{2}}{13675754015223831}\approx 3093.778984312$$

Solution Steps

Divide \frac{4\pi ^{2}\times \left(2.28\times 10^{8}\right)^{3}}{\left(687\times 24\times 60\times 60\right)^{2}} by \frac{3.72\times 6794^{2}}{4} by multiplying \frac{4\pi ^{2}\times \left(2.28\times 10^{8}\right)^{3}}{\left(687\times 24\times 60\times 60\right)^{2}} by the reciprocal of \frac{3.72\times 6794^{2}}{4}.

$$\frac{4\pi ^{2}\times \left(2.28\times 10^{8}\right)^{3}\times 4}{\left(687\times 24\times 60\times 60\right)^{2}\times 3.72\times 6794^{2}}$$

Calculate 10 to the power of 8 and get 100000000.

$$\frac{4\pi ^{2}\times \left(2.28\times 100000000\right)^{3}\times 4}{\left(687\times 24\times 60\times 60\right)^{2}\times 3.72\times 6794^{2}}$$

Multiply 2.28 and 100000000 to get 228000000.

$$\frac{4\pi ^{2}\times 228000000^{3}\times 4}{\left(687\times 24\times 60\times 60\right)^{2}\times 3.72\times 6794^{2}}$$

Calculate 228000000 to the power of 3 and get 11852352000000000000000000.

$$\frac{4\pi ^{2}\times 11852352000000000000000000\times 4}{\left(687\times 24\times 60\times 60\right)^{2}\times 3.72\times 6794^{2}}$$

Multiply 4 and 11852352000000000000000000 to get 47409408000000000000000000.

$$\frac{47409408000000000000000000\pi ^{2}\times 4}{\left(687\times 24\times 60\times 60\right)^{2}\times 3.72\times 6794^{2}}$$

Multiply 47409408000000000000000000 and 4 to get 189637632000000000000000000.

$$\frac{189637632000000000000000000\pi ^{2}}{\left(687\times 24\times 60\times 60\right)^{2}\times 3.72\times 6794^{2}}$$

Multiply 687 and 24 to get 16488.

$$\frac{189637632000000000000000000\pi ^{2}}{\left(16488\times 60\times 60\right)^{2}\times 3.72\times 6794^{2}}$$

Multiply 16488 and 60 to get 989280.

$$\frac{189637632000000000000000000\pi ^{2}}{\left(989280\times 60\right)^{2}\times 3.72\times 6794^{2}}$$

Multiply 989280 and 60 to get 59356800.

$$\frac{189637632000000000000000000\pi ^{2}}{59356800^{2}\times 3.72\times 6794^{2}}$$

Calculate 59356800 to the power of 2 and get 3523229706240000.

$$\frac{189637632000000000000000000\pi ^{2}}{3523229706240000\times 3.72\times 6794^{2}}$$

Multiply 3523229706240000 and 3.72 to get 13106414507212800.

$$\frac{189637632000000000000000000\pi ^{2}}{13106414507212800\times 6794^{2}}$$

Calculate 6794 to the power of 2 and get 46158436.

$$\frac{189637632000000000000000000\pi ^{2}}{13106414507212800\times 46158436}$$

Multiply 13106414507212800 and 46158436 to get 604971595220653567180800.

$$\frac{189637632000000000000000000\pi ^{2}}{604971595220653567180800}$$

Divide 189637632000000000000000000\pi ^{2} by 604971595220653567180800 to get \frac{4286875000000000000}{13675754015223831}\pi ^{2}.

$$\frac{4286875000000000000}{13675754015223831}\pi ^{2}$$

Expand

$$\frac{4286875000000000000 \pi ^ {2}}{13675754015223831} = 3093\frac{10653197832629768}{13675754015223832} = 3093.778984312$$

Solution Steps

Divide \frac{4\pi ^{2}\times \left(2.28\times 10^{8}\right)^{3}}{\left(687\times 24\times 60\times 60\right)^{2}} by \frac{3.72\times 6794^{2}}{4} by multiplying \frac{4\pi ^{2}\times \left(2.28\times 10^{8}\right)^{3}}{\left(687\times 24\times 60\times 60\right)^{2}} by the reciprocal of \frac{3.72\times 6794^{2}}{4}.

$$\frac{4\pi ^{2}\times \left(2.28\times 10^{8}\right)^{3}\times 4}{\left(687\times 24\times 60\times 60\right)^{2}\times 3.72\times 6794^{2}}$$

Calculate 10 to the power of 8 and get 100000000.

$$\frac{4\pi ^{2}\times \left(2.28\times 100000000\right)^{3}\times 4}{\left(687\times 24\times 60\times 60\right)^{2}\times 3.72\times 6794^{2}}$$

Multiply 2.28 and 100000000 to get 228000000.

$$\frac{4\pi ^{2}\times 228000000^{3}\times 4}{\left(687\times 24\times 60\times 60\right)^{2}\times 3.72\times 6794^{2}}$$

Calculate 228000000 to the power of 3 and get 11852352000000000000000000.

$$\frac{4\pi ^{2}\times 11852352000000000000000000\times 4}{\left(687\times 24\times 60\times 60\right)^{2}\times 3.72\times 6794^{2}}$$

Multiply 4 and 11852352000000000000000000 to get 47409408000000000000000000.

$$\frac{47409408000000000000000000\pi ^{2}\times 4}{\left(687\times 24\times 60\times 60\right)^{2}\times 3.72\times 6794^{2}}$$

Multiply 47409408000000000000000000 and 4 to get 189637632000000000000000000.

$$\frac{189637632000000000000000000\pi ^{2}}{\left(687\times 24\times 60\times 60\right)^{2}\times 3.72\times 6794^{2}}$$

Multiply 687 and 24 to get 16488.

$$\frac{189637632000000000000000000\pi ^{2}}{\left(16488\times 60\times 60\right)^{2}\times 3.72\times 6794^{2}}$$

Multiply 16488 and 60 to get 989280.

$$\frac{189637632000000000000000000\pi ^{2}}{\left(989280\times 60\right)^{2}\times 3.72\times 6794^{2}}$$

Multiply 989280 and 60 to get 59356800.

$$\frac{189637632000000000000000000\pi ^{2}}{59356800^{2}\times 3.72\times 6794^{2}}$$

Calculate 59356800 to the power of 2 and get 3523229706240000.

$$\frac{189637632000000000000000000\pi ^{2}}{3523229706240000\times 3.72\times 6794^{2}}$$

Multiply 3523229706240000 and 3.72 to get 13106414507212800.

$$\frac{189637632000000000000000000\pi ^{2}}{13106414507212800\times 6794^{2}}$$

Calculate 6794 to the power of 2 and get 46158436.

$$\frac{189637632000000000000000000\pi ^{2}}{13106414507212800\times 46158436}$$

Multiply 13106414507212800 and 46158436 to get 604971595220653567180800.

$$\frac{189637632000000000000000000\pi ^{2}}{604971595220653567180800}$$

Divide 189637632000000000000000000\pi ^{2} by 604971595220653567180800 to get \frac{4286875000000000000}{13675754015223831}\pi ^{2}.

$$\frac{4286875000000000000}{13675754015223831}\pi ^{2}$$