# Find the curved surface area and volume of a cylinder whose height and radius are (a)15 cm and 4 cm respectively. (b) 17cm and 5.5cm respectively.

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Hint: A cylinder is a three dimensional solid. A cylinder is one of the basic curved geometric shapes, with the surface formed by the points at a fixed distance from a given line segment, Known as the axis of the cylinder.
Volume of cylinder $=\pi {{r}^{2}}h$
Curved surface area $=2\pi rh$
Where r is the radius and h is the height
of the cylinder.

From the given question we have following information for part (a)
Height of cylinder $h=15cm$
Radius of cylinder $r=4cm$
We have to find the curved surface area of cylinder
Curved surface area $=2\pi rh$
Now here we substitute the value of r and h

Curved surface area
\begin{align} & =(2)\left( \dfrac{22}{7} \right)(4cm)(15cm) \\ & =377.142c{{m}^{2}} \\ \end{align}
Volume of cylinder
\begin{align} & =\pi {{r}^{2}}h \\ & =\left( \dfrac{22}{7} \right)\left( {{4}^{2}} \right)\left( 15 \right) \\ & =754.28c{{m}^{3}} \\ \end{align}
From the given question we have following information for part (b)
Height of cylinder $h=17cm$
Radius of cylinder $r=5.5cm$
We have to find the curved surface area of cylinder
Curved surface area $=2\pi rh$
Now here we substitute the value of r and h
Curved surface area
\begin{align} & =(2)\left( \dfrac{22}{7} \right)(5.5cm)(17cm) \\ & =587.71c{{m}^{2}} \\ \end{align}
Volume of cylinder
\begin{align} & =\pi {{r}^{2}}h \\ & =\left( \dfrac{22}{7} \right){{\left( 5.5 \right)}^{2}}\left( 17 \right) \\ & =1616.21c{{m}^{3}} \\ \end{align}

Note: We should be cautious about the total surface area and curved surface area of the cylinder.
In the total surface area we have to add two circular areas that are for top and bottom.
$TSA=CSA+2\pi {{r}^{2}}$
Also take care of unit of area $(c{{m}^{2}})$ and unit of volume $(c{{m}^{3}})$