Solve pi*(20*40*0.4+30*40*0.3+0.5*(20^2+30^2)*0.2)

$$\pi \times (20 \times 40 \times 0.4+30 \times 40 \times 0.3+0.5 \times ( { 20 }^{ 2 } + { 30 }^{ 2 } ) \times 0.2)$$

Evaluate

$$810\pi \approx 2544.690049408$$

Solution Steps

Multiply 20 and 40 to get 800. Multiply 30 and 40 to get 1200.

$$\pi \left(800\times 0.4+1200\times 0.3+0.5\left(20^{2}+30^{2}\right)\times 0.2\right)$$

Multiply 800 and 0.4 to get 320.

$$\pi \left(320+1200\times 0.3+0.5\left(20^{2}+30^{2}\right)\times 0.2\right)$$

Multiply 1200 and 0.3 to get 360.

$$\pi \left(320+360+0.5\left(20^{2}+30^{2}\right)\times 0.2\right)$$

Add 320 and 360 to get 680.

$$\pi \left(680+0.5\left(20^{2}+30^{2}\right)\times 0.2\right)$$

Calculate 20 to the power of 2 and get 400.

$$\pi \left(680+0.5\left(400+30^{2}\right)\times 0.2\right)$$

Calculate 30 to the power of 2 and get 900.

$$\pi \left(680+0.5\left(400+900\right)\times 0.2\right)$$

Add 400 and 900 to get 1300.

$$\pi \left(680+0.5\times 1300\times 0.2\right)$$

Multiply 0.5 and 1300 to get 650.

$$\pi \left(680+650\times 0.2\right)$$

Multiply 650 and 0.2 to get 130.

$$\pi \left(680+130\right)$$

Add 680 and 130 to get 810.

$$\pi \times 810$$

Expand

$$810\pi$$

Solution Steps

Multiply 20 and 40 to get 800. Multiply 30 and 40 to get 1200.

$$\pi \left(800\times 0.4+1200\times 0.3+0.5\left(20^{2}+30^{2}\right)\times 0.2\right)$$

Multiply 800 and 0.4 to get 320.

$$\pi \left(320+1200\times 0.3+0.5\left(20^{2}+30^{2}\right)\times 0.2\right)$$

Multiply 1200 and 0.3 to get 360.

$$\pi \left(320+360+0.5\left(20^{2}+30^{2}\right)\times 0.2\right)$$

Add 320 and 360 to get 680.

$$\pi \left(680+0.5\left(20^{2}+30^{2}\right)\times 0.2\right)$$

Calculate 20 to the power of 2 and get 400.

$$\pi \left(680+0.5\left(400+30^{2}\right)\times 0.2\right)$$

Calculate 30 to the power of 2 and get 900.

$$\pi \left(680+0.5\left(400+900\right)\times 0.2\right)$$

Add 400 and 900 to get 1300.

$$\pi \left(680+0.5\times 1300\times 0.2\right)$$

Multiply 0.5 and 1300 to get 650.

$$\pi \left(680+650\times 0.2\right)$$

Multiply 650 and 0.2 to get 130.

$$\pi \left(680+130\right)$$

Add 680 and 130 to get 810.

$$\pi \times 810$$