Questions & Answers: "Volume and Surface Area"

The diameter of the cylindrical tank is $7$m, so the radius $r = \frac{7}{2}$m. The height $h = 2$m. The volume (capacity) of the cylinder is given by $V = \pi r^2 h$. Substituting the values, $V = \frac{22}{7} \times (\frac{7}{2})^2 \times 2 = \frac{22}{7} \times \frac{49}{4} \times 2 = \frac{22 \times 7 \times 2}{4} = \frac{11 \times 7 \times 2}{2} = 77$ cubic m. Since $1$ cubic m $= 1000$ litres, the capacity in litres is $77 \times 1000 = 77000$ litres.

The formula for the volume of a cone ($V$) is $V = \frac{1}{3} \pi r^2 h$, where $r$ is the radius of the base and $h$ is the height. Given: Radius ($r$) = 21 cm Height ($h$) = 20 cm Using $\pi = \frac{22}{7}$:$V = \frac{1}{3} \times \frac{22}{7} \times (21\text{ cm})^2 \times 20\text{ cm}$ $V = \frac{1}{3} \times \frac{22}{7} \times 21 \times 21 \times 20$ We can simplify the calculation: $V = \frac{1}{3} \times 22 \times \left(\frac{21}{7}\right) \times 21 \times 20$ $V = \frac{1}{3} \times 22 \times 3 \times 21 \times 20$Cancel out the $3$ in the denominator and numerator:$V = 22 \times 21 \times 20$First, calculate $22 \times 21$:$22 \times 21 = 462$Now, multiply by $20$:$V = 462 \times 20 = 9240$Therefore, the volume of the cone is $9240$ cubic cm.