(a) The curved surface area of a right circular cylinder is 176 sq cm and its volume is 1232 cu cm. What is the height of the cylinder?

Let $\displaystyle h$ be the height of cylinder CSA of cylinder $\displaystyle =176 \Rightarrow 2 \pi r h=176 \ldots(i)$ Volume of cylinder $\displaystyle =1232 \Rightarrow \pi r^{2} h=1232$ on dividing, $\displaystyle \frac{\pi r^{\not 2} h}{2 \pi r h}=\frac{1232}{176}$ we get, $\displaystyle r=14 \mathrm{~cm}$ \[\begin{array}{l} \therefore(i) \Rightarrow 2 \times \frac{22}{7} \times 14^{2} \times h=176 \\ \Rightarrow h=2 \mathrm{~cm} \end{array} \]OrThe largest sphere is carved out of a solid cube of side $\displaystyle 21$ cm. Find the volume of the sphere.Diameter of sphere = side of cube $\displaystyle =21 \mathrm{~cm}$ ∴ radius $\displaystyle r=\frac{21}{2} \mathrm{~cm}$ Volume of sphere $\displaystyle =\frac{4}{3} \pi r^{3}=\frac{4}{3} \times \frac{22}{7} \times \frac{21}{2} \times \frac{21}{2} \times \frac{21}{2}$ \[=4851 \mathrm{~cm}^{3} \]SECTION-B