Solve pi102^2h=4/3pi87.5^3

$$\pi { 102 }^{ 2 } h = \frac{ 4 }{ 3 } \pi { 87.5 }^{ 3 }$$

Solve for h

$$h = \frac{5359375}{62424} = 85\frac{53335}{62424} \approx 85.854398949$$

Steps for Solving Linear Equation

Cancel out \pi on both sides.

$$102^{2}h=\frac{4}{3}\times 87.5^{3}$$

Calculate 102 to the power of 2 and get 10404.

$$10404h=\frac{4}{3}\times 87.5^{3}$$

Calculate 87.5 to the power of 3 and get 669921.875.

$$10404h=\frac{4}{3}\times 669921.875$$

Convert decimal number 669921.875 to fraction \frac{669921875}{1000}. Reduce the fraction \frac{669921875}{1000} to lowest terms by extracting and canceling out 125.

$$10404h=\frac{4}{3}\times \frac{5359375}{8}$$

Multiply \frac{4}{3} times \frac{5359375}{8} by multiplying numerator times numerator and denominator times denominator.

$$10404h=\frac{4\times 5359375}{3\times 8}$$

Do the multiplications in the fraction \frac{4\times 5359375}{3\times 8}.

$$10404h=\frac{21437500}{24}$$

Reduce the fraction \frac{21437500}{24} to lowest terms by extracting and canceling out 4.

$$10404h=\frac{5359375}{6}$$

Divide both sides by 10404.

$$h=\frac{\frac{5359375}{6}}{10404}$$

Express \frac{\frac{5359375}{6}}{10404} as a single fraction.

$$h=\frac{5359375}{6\times 10404}$$

Multiply 6 and 10404 to get 62424.

$$h=\frac{5359375}{62424}$$