question_answer

 

(a) A cylindrical tank has a capacity of 5632\[{{m}^{3}}\]. If the diameter of its base is 16 m. Find its depth.

(b) If side of square is 14 cm, then find the area of semi-circle as shown in the figure.

Answer:

(a) Let the depth of the cylindrical tank = h

and Radius of its base (r) = 8 m

Then,     the capacity of the tank = Volume of the tank

\[=\pi {{r}^{2}}h\]

\[=\frac{22}{7}\times 8\times 8h\]

Thus,         \[\frac{22}{7}\times 8\times 8\times h=5632\]

or                        \[h=\frac{5632\times 7}{22\times 8\times 8}\]

or                            h =28m

Hence, the depth of the cylindrical tank = 28 m

(b)  Since side of square = 14 cm

Then,      diameter of semi-circle = 14 cm

Therefore, radius of semi-circle (r)\[=\frac{14}{2}\]

= 7cm

Thus,      Area of semi-circle \[=\frac{1}{2}\times \pi {{r}^{2}}\]

\[=\frac{1}{2}\times \frac{22}{7}\times {{7}^{2}}\]

\[=\frac{11}{7}\times 7\times 7\]

= 77 \[c{{m}^{2}}\]