Solve 1/3*3.14*h[(20)^2+(12)^2+20*12]=12308.8

$$\frac { 1 } { 3 } \times 3.14 \times h [ ( 20 ) ^ { 2 } + ( 12 ) ^ { 2 } + 20 \times 12 ] = 12308.8$$

Solve for h

$$h=15$$

Steps for Solving Linear Equation

Convert decimal number 3.14 to fraction \frac{314}{100}. Reduce the fraction \frac{314}{100} to lowest terms by extracting and canceling out 2.

$$\frac{1}{3}\times \frac{157}{50}h\left(20^{2}+12^{2}+20\times 12\right)=12308.8$$

Multiply \frac{1}{3} times \frac{157}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 157}{3\times 50}h\left(20^{2}+12^{2}+20\times 12\right)=12308.8$$

Do the multiplications in the fraction \frac{1\times 157}{3\times 50}.

$$\frac{157}{150}h\left(20^{2}+12^{2}+20\times 12\right)=12308.8$$

Calculate 20 to the power of 2 and get 400.

$$\frac{157}{150}h\left(400+12^{2}+20\times 12\right)=12308.8$$

Calculate 12 to the power of 2 and get 144.

$$\frac{157}{150}h\left(400+144+20\times 12\right)=12308.8$$

Add 400 and 144 to get 544.

$$\frac{157}{150}h\left(544+20\times 12\right)=12308.8$$

Multiply 20 and 12 to get 240.

$$\frac{157}{150}h\left(544+240\right)=12308.8$$

Add 544 and 240 to get 784.

$$\frac{157}{150}h\times 784=12308.8$$

Express \frac{157}{150}\times 784 as a single fraction.

$$\frac{157\times 784}{150}h=12308.8$$

Multiply 157 and 784 to get 123088.

$$\frac{123088}{150}h=12308.8$$

Reduce the fraction \frac{123088}{150} to lowest terms by extracting and canceling out 2.

$$\frac{61544}{75}h=12308.8$$

Multiply both sides by \frac{75}{61544}, the reciprocal of \frac{61544}{75}.

$$h=12308.8\times \frac{75}{61544}$$

Convert decimal number 12308.8 to fraction \frac{123088}{10}. Reduce the fraction \frac{123088}{10} to lowest terms by extracting and canceling out 2.

$$h=\frac{61544}{5}\times \frac{75}{61544}$$

Multiply \frac{61544}{5} times \frac{75}{61544} by multiplying numerator times numerator and denominator times denominator.

$$h=\frac{61544\times 75}{5\times 61544}$$

Cancel out 61544 in both numerator and denominator.

$$h=\frac{75}{5}$$

Divide 75 by 5 to get 15.

$$h=15$$