Solve (pi*(1/2x)^2*y+pi(1/2*2x)^2*y)div(pi(1/2*1/2x)^2*8)

$$( \pi \times ( \frac { 1 } { 2 } x ) ^ { 2 } \times y + \pi ( \frac { 1 } { 2 } \times 2 x ) ^ { 2 } \times y ) \div ( \pi ( \frac { 1 } { 2 } \times \frac { 1 } { 2 } x ) ^ { 2 } \times 8 )$$

Evaluate

$$\frac{5y}{2}$$

Solution Steps

Expand \left(\frac{1}{2}x\right)^{2}.

$$\frac{\pi \times \left(\frac{1}{2}\right)^{2}x^{2}y+\pi \times \left(\frac{1}{2}\times 2x\right)^{2}y}{\pi \times \left(\frac{1}{2}\times \frac{1}{2}x\right)^{2}\times 8}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{\pi \times \frac{1}{4}x^{2}y+\pi \times \left(\frac{1}{2}\times 2x\right)^{2}y}{\pi \times \left(\frac{1}{2}\times \frac{1}{2}x\right)^{2}\times 8}$$

Multiply \frac{1}{2} and 2 to get 1.

$$\frac{\pi \times \frac{1}{4}x^{2}y+\pi x^{2}y}{\pi \times \left(\frac{1}{2}\times \frac{1}{2}x\right)^{2}\times 8}$$

Combine \pi \times \frac{1}{4}x^{2}y and \pi x^{2}y to get \frac{5}{4}\pi x^{2}y.

$$\frac{\frac{5}{4}\pi x^{2}y}{\pi \times \left(\frac{1}{2}\times \frac{1}{2}x\right)^{2}\times 8}$$

Multiply \frac{1}{2} and \frac{1}{2} to get \frac{1}{4}.

$$\frac{\frac{5}{4}\pi x^{2}y}{\pi \times \left(\frac{1}{4}x\right)^{2}\times 8}$$

Expand \left(\frac{1}{4}x\right)^{2}.

$$\frac{\frac{5}{4}\pi x^{2}y}{\pi \times \left(\frac{1}{4}\right)^{2}x^{2}\times 8}$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{\frac{5}{4}\pi x^{2}y}{\pi \times \frac{1}{16}x^{2}\times 8}$$

Multiply \frac{1}{16} and 8 to get \frac{1}{2}.

$$\frac{\frac{5}{4}\pi x^{2}y}{\pi \times \frac{1}{2}x^{2}}$$

Cancel out \pi x^{2} in both numerator and denominator.

$$\frac{\frac{5}{4}y}{\frac{1}{2}}$$

Divide \frac{5}{4}y by \frac{1}{2} by multiplying \frac{5}{4}y by the reciprocal of \frac{1}{2}.

$$\frac{5}{4}y\times 2$$

Multiply \frac{5}{4} and 2 to get \frac{5}{2}.

$$\frac{5}{2}y$$

Expand

$$\frac{5y}{2}$$

Solution Steps

Expand \left(\frac{1}{2}x\right)^{2}.

$$\frac{\pi \times \left(\frac{1}{2}\right)^{2}x^{2}y+\pi \times \left(\frac{1}{2}\times 2x\right)^{2}y}{\pi \times \left(\frac{1}{2}\times \frac{1}{2}x\right)^{2}\times 8}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{\pi \times \frac{1}{4}x^{2}y+\pi \times \left(\frac{1}{2}\times 2x\right)^{2}y}{\pi \times \left(\frac{1}{2}\times \frac{1}{2}x\right)^{2}\times 8}$$

Multiply \frac{1}{2} and 2 to get 1.

$$\frac{\pi \times \frac{1}{4}x^{2}y+\pi x^{2}y}{\pi \times \left(\frac{1}{2}\times \frac{1}{2}x\right)^{2}\times 8}$$

Combine \pi \times \frac{1}{4}x^{2}y and \pi x^{2}y to get \frac{5}{4}\pi x^{2}y.

$$\frac{\frac{5}{4}\pi x^{2}y}{\pi \times \left(\frac{1}{2}\times \frac{1}{2}x\right)^{2}\times 8}$$

Multiply \frac{1}{2} and \frac{1}{2} to get \frac{1}{4}.

$$\frac{\frac{5}{4}\pi x^{2}y}{\pi \times \left(\frac{1}{4}x\right)^{2}\times 8}$$

Expand \left(\frac{1}{4}x\right)^{2}.

$$\frac{\frac{5}{4}\pi x^{2}y}{\pi \times \left(\frac{1}{4}\right)^{2}x^{2}\times 8}$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{\frac{5}{4}\pi x^{2}y}{\pi \times \frac{1}{16}x^{2}\times 8}$$

Multiply \frac{1}{16} and 8 to get \frac{1}{2}.

$$\frac{\frac{5}{4}\pi x^{2}y}{\pi \times \frac{1}{2}x^{2}}$$

Cancel out \pi x^{2} in both numerator and denominator.

$$\frac{\frac{5}{4}y}{\frac{1}{2}}$$

Divide \frac{5}{4}y by \frac{1}{2} by multiplying \frac{5}{4}y by the reciprocal of \frac{1}{2}.

$$\frac{5}{4}y\times 2$$

Multiply \frac{5}{4} and 2 to get \frac{5}{2}.

$$\frac{5}{2}y$$