Question

The curved surface area of a cylinder is $113.04m^2$. The area of one of the bases is $15.2m^2$. Find the height of the cylinder. (use $\pi =3.14$). And also find its surface area of a cylinder.

• A. $141.21m^2,2m$
• B. $143.44m^2,8m$
• C. $143.23m^2,7m$
• D. $104.23m^2,6m$

Answer 1

The correct option is B $143.44m^2,8m$

Formula

Curved surface area of cylinder$=2\pi rh$

Area of base$=\pi r^2$

where,

$r=radius$

$h=height$

Surface area of cylinder is$=2\pi r^2+2\pi rh$

We know that $2\pi rh=113.04m^2$

and $\pi r^2=15.2m^2$

$\therefore surfaceareaofcylinder=2\ast 15.2+113.04=30.4+113.04=143.44m^3$

Area of base$=\pi r^2$

$\therefore 15.2=3.14\ast r^2$

$\Rightarrow r^2=4.840$

$\Rightarrow r=\sqrt{4.840}$

$\Rightarrow r=2.2m$

Curved surface area of cylinder$=2\pi rh$

$\Rightarrow 113.04=2\ast 3.14\ast 2.2\ast h$

$\Rightarrow 113.04=13.816\ast h$

$\Rightarrow h=\frac{113.04}{13.816}$

$\Rightarrow h=8m$