Solve 3.14*(30div2)^2*6+3.14*(3.0div2)^2*6div3

$$3.14 \times ( 30 \div 2 ) ^ { 2 } \times 6 + 3.14 \times ( 3.0 \div 2 ) ^ { 2 } \times 6 \div 3$$

Evaluate

$$4253.13$$

Solution Steps

Divide 30 by 2 to get 15.

$$3.14\times 15^{2}\times 6+\frac{3.14\times \left(\frac{3}{2}\right)^{2}\times 6}{3}$$

Calculate 15 to the power of 2 and get 225.

$$3.14\times 225\times 6+\frac{3.14\times \left(\frac{3}{2}\right)^{2}\times 6}{3}$$

Multiply 3.14 and 225 to get 706.5.

$$706.5\times 6+\frac{3.14\times \left(\frac{3}{2}\right)^{2}\times 6}{3}$$

Multiply 706.5 and 6 to get 4239.

$$4239+\frac{3.14\times \left(\frac{3}{2}\right)^{2}\times 6}{3}$$

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$4239+\frac{3.14\times \frac{9}{4}\times 6}{3}$$

Multiply 3.14 and \frac{9}{4} to get \frac{1413}{200}.

$$4239+\frac{\frac{1413}{200}\times 6}{3}$$

Multiply \frac{1413}{200} and 6 to get \frac{4239}{100}.

$$4239+\frac{\frac{4239}{100}}{3}$$

Express \frac{\frac{4239}{100}}{3} as a single fraction.

$$4239+\frac{4239}{100\times 3}$$

Multiply 100 and 3 to get 300.

$$4239+\frac{4239}{300}$$

Reduce the fraction \frac{4239}{300} to lowest terms by extracting and canceling out 3.

$$4239+\frac{1413}{100}$$

Add 4239 and \frac{1413}{100} to get \frac{425313}{100}.

$$\frac{425313}{100}$$

Factor

$$\frac{7 \cdot 43 \cdot 157 \cdot 3 ^ {2}}{2 ^ {2} \cdot 5 ^ {2}} = 4253\frac{13}{100} = 4253.13$$