Question

2.
The curved surface area of a cylinder is 440 cm. Find
its volume if the height of it is 21 cm.​

Answer 1

Given:

• CSA of cylinder = 440 cm
• Height = 21 cm

To find:

➜ Volume = ?

Method:

$\large{\sf{\star \: CSA \: of\: cylinder = 2 \pi r h}}\\\\\\\Rightarrow \sf{440 = 2 \times \dfrac{22}{7} \times r \times 21}\\\\\\\Rightarrow \sf{440 = 2 \times 22 \times 3r}\\\\\\\Rightarrow \sf{440 = 132r}\\\\\\\Rightarrow \sf{r = \dfrac{440}{132}}\\\\\\\therefore \underline{\bf{r = 3.3 \: cm}}$

$\rm{Now \: let's \: find \: volume;}$

$\large{\sf{Volume\: of\: cylinder = \pi r^{2}h}}\\\\\\\Rightarrow \sf{Volume = \dfrac{22}{7} \times (3.3)^{2} \times 21}\\\\\\\Rightarrow \sf{Volume = \dfrac{22}{7} \times 10.89 \times 21}\\\\\\\Rightarrow \sf{Volume = 22 \times 10.89 \times 3}\\\\\\\therefore \boxed{\bf{Volume = 718.74 \: cm}}$

Additional Information:

$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}$