Solve =1/3*22/7*14[(35/2)^2+(30/2)^2+(frac{35}{2}*frac{30}{2})]cm^3

$$= \frac { 1 } { 3 } \times \frac { 22 } { 7 } \times 14 [ ( \frac { 35 } { 2 } ) ^ { 2 } + ( \frac { 30 } { 2 } ) ^ { 2 } + ( \frac { 35 } { 2 } \times \frac { 30 } { 2 } ) ] cm ^ { 3 }$$

Evaluate

$$\frac{34925cm^{3}}{3}$$

Solution Steps

Multiply \frac{1}{3} and \frac{22}{7} to get \frac{22}{21}.

$$\frac{22}{21}\times 14\left(\left(\frac{35}{2}\right)^{2}+\left(\frac{30}{2}\right)^{2}+\frac{35}{2}\times \frac{30}{2}\right)cm^{3}$$

Multiply \frac{22}{21} and 14 to get \frac{44}{3}.

$$\frac{44}{3}\left(\left(\frac{35}{2}\right)^{2}+\left(\frac{30}{2}\right)^{2}+\frac{35}{2}\times \frac{30}{2}\right)cm^{3}$$

Calculate \frac{35}{2} to the power of 2 and get \frac{1225}{4}.

$$\frac{44}{3}\left(\frac{1225}{4}+\left(\frac{30}{2}\right)^{2}+\frac{35}{2}\times \frac{30}{2}\right)cm^{3}$$

Divide 30 by 2 to get 15.

$$\frac{44}{3}\left(\frac{1225}{4}+15^{2}+\frac{35}{2}\times \frac{30}{2}\right)cm^{3}$$

Calculate 15 to the power of 2 and get 225.

$$\frac{44}{3}\left(\frac{1225}{4}+225+\frac{35}{2}\times \frac{30}{2}\right)cm^{3}$$

Add \frac{1225}{4} and 225 to get \frac{2125}{4}.

$$\frac{44}{3}\left(\frac{2125}{4}+\frac{35}{2}\times \frac{30}{2}\right)cm^{3}$$

Divide 30 by 2 to get 15.

$$\frac{44}{3}\left(\frac{2125}{4}+\frac{35}{2}\times 15\right)cm^{3}$$

Multiply \frac{35}{2} and 15 to get \frac{525}{2}.

$$\frac{44}{3}\left(\frac{2125}{4}+\frac{525}{2}\right)cm^{3}$$

Add \frac{2125}{4} and \frac{525}{2} to get \frac{3175}{4}.

$$\frac{44}{3}\times \frac{3175}{4}cm^{3}$$

Multiply \frac{44}{3} and \frac{3175}{4} to get \frac{34925}{3}.

$$\frac{34925}{3}cm^{3}$$

Expand

$$\frac{34925cm^{3}}{3}$$

Solution Steps

Multiply \frac{1}{3} and \frac{22}{7} to get \frac{22}{21}.

$$\frac{22}{21}\times 14\left(\left(\frac{35}{2}\right)^{2}+\left(\frac{30}{2}\right)^{2}+\frac{35}{2}\times \frac{30}{2}\right)cm^{3}$$

Multiply \frac{22}{21} and 14 to get \frac{44}{3}.

$$\frac{44}{3}\left(\left(\frac{35}{2}\right)^{2}+\left(\frac{30}{2}\right)^{2}+\frac{35}{2}\times \frac{30}{2}\right)cm^{3}$$

Calculate \frac{35}{2} to the power of 2 and get \frac{1225}{4}.

$$\frac{44}{3}\left(\frac{1225}{4}+\left(\frac{30}{2}\right)^{2}+\frac{35}{2}\times \frac{30}{2}\right)cm^{3}$$

Divide 30 by 2 to get 15.

$$\frac{44}{3}\left(\frac{1225}{4}+15^{2}+\frac{35}{2}\times \frac{30}{2}\right)cm^{3}$$

Calculate 15 to the power of 2 and get 225.

$$\frac{44}{3}\left(\frac{1225}{4}+225+\frac{35}{2}\times \frac{30}{2}\right)cm^{3}$$

Add \frac{1225}{4} and 225 to get \frac{2125}{4}.

$$\frac{44}{3}\left(\frac{2125}{4}+\frac{35}{2}\times \frac{30}{2}\right)cm^{3}$$

Divide 30 by 2 to get 15.

$$\frac{44}{3}\left(\frac{2125}{4}+\frac{35}{2}\times 15\right)cm^{3}$$

Multiply \frac{35}{2} and 15 to get \frac{525}{2}.

$$\frac{44}{3}\left(\frac{2125}{4}+\frac{525}{2}\right)cm^{3}$$

Add \frac{2125}{4} and \frac{525}{2} to get \frac{3175}{4}.

$$\frac{44}{3}\times \frac{3175}{4}cm^{3}$$

Multiply \frac{44}{3} and \frac{3175}{4} to get \frac{34925}{3}.

$$\frac{34925}{3}cm^{3}$$