Question

The curved surface area of a cylinder is 176 square cm and its area of the base is 38.5 square cm . Find its radius and height. ​

Answer 1

Solution :

$\underline{\bf{Given\::}}$

• Curved surface area of cylinder = 176 cm² .
• Area of the base = 38.5 cm²

$\underline{\bf{Explanation\::}}$

As we know that formula of the area of the base of cylinder;

$\boxed{\bf{Base=\pi r^{2}}}$

$\mapsto\sf{\pi r^{2} = 38.5}\\\\\mapsto\sf{22/7 \times r^{2} = 38.5}\\\\\mapsto\sf{r^{2} = 38.5\times 7/22}\\\\\mapsto\sf{r^{2} = \cancel{269.5/22}}\\\\\mapsto\sf{r^{2} = 12.25}\\\\\mapsto\sf{r=\sqrt{12.25} }\\\\\mapsto\bf{r=3.5\:cm}$

As we know that formula of the curved surface area of the cylinder;

$\boxed{\bf{C.S.A = 2\pi rh\:\:\:(sq.unit)}}$

$\mapsto\sf{2\times 22/7\times 3.5 \times h=176}\\\\\mapsto\sf{44/\cancel{7 }\times \cancel{3.5} \times h=176}\\\\\mapsto\sf{44\times 0.5\times h=176}\\\\\mapsto\sf{22h=176}\\\\\mapsto\sf{h=\cancel{176/22}}\\\\\mapsto\bf{h=8\:cm}$

Thus;

The radius & height of the cylinder will be 3.5 cm & 8 cm .

Answer 2

GIVEN :-

• Curved surface area of the cylinder = 176 cm

• Base area of the cylinder = 38.5 cm²

TO FIND :-

• Radius of the cylinder .

• Height of the cylinder .

SOLUTION :-

 $\bullet \ \sf Base \ area \ of \ the \ cylinder = \pi r^2$

        $\longrightarrow\sf \pi r^2 = 38.5 \\\\\longrightarrow r^2 =\dfrac{38.5 \times 7}{22}\\\\\longrightarrow r^2= 12.25\\\\\longrightarrow r = \sqrt{12.25 } \\\\\longrightarrow\bf r = 3.5$

$\bullet \ \sf Curved \ surface \ area \ of \ the \ cylinder = 2\pi r h$

       $\longrightarrow\sf 2\pi \times 3.5 \times h =176 \\\\\longrightarrow h = \dfrac{176 \times 7 }{2 \times 22 \times 3.5 }\\\\\longrightarrow \sf h = \dfrac{1232}{154}\\\\\longrightarrow \bf h = 8$

 Radius of the cylinder = 3.5 cm

 Height of the cylinder = 8 cm