Question

the CSA of a cylinder is 880 cm^2.If the height of the cylinder is 1m,Find the diameter of the base

Answer 1

Given:

• CSA of cylinder = 880 cm²
• Height of cylinder = 1 m

To find:

➵ Diameter of base = ?

Formulas used:

★ CSA of cylinder = 2πrh

★ Diameter = 2 × Radius

Solution:

$\large{\sf{\boxed{\underline{\sf{CSA = 2 \pi r h}}}}}$

$\large{\Rightarrow \: \sf{880 = 2 \pi r \times 1}}\\\\\\\large{\Rightarrow \: \sf{880 = 2 \times \dfrac{22}{7} \times r}}\\\\\\\large{\Rightarrow \: \sf{880 = \dfrac{44r}{7}}}\\\\\\\large{\Rightarrow \: \sf{44r = 880 \times 7}}\\\\\\\large{\Rightarrow \: \sf{r = \dfrac{880 \times 7}{44}}}\\\\\\\\\large{\therefore \: \boxed{\sf{r = 140\: cm}}}$

$\\\\\underbrace{\sf{For \: finding \: diameter,}}\\\\\\\large{\bf{Diameter = 2 \times radius}}$

$\large{\sf{\Rightarrow Diameter = 2 \times 140}}\\\\\\\therefore \large{\boxed{\boxed{\bf{Diameter = 280 \: cm}}}}$

Know more:

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